BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.7//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1988@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260306T132609 DTSTART;TZID=Europe/Zurich:20260310T103000 SUMMARY:Seminar Algebra and Geometry: Claudia Stadlmayr (Universität Neuch âtel) DESCRIPTION:Group schemes provide a refined notion of symmetry in positive characteristic: they detect infinitesimal structure invisible to the discr ete automorphism group. Classical examples such as mu_p or alpha_p equip t he trivial topological space with a non-trivial algebraic structure.In thi s talk I will explain how this perspective can be used to classify weak an d RDP del Pezzo surfaces admitting global vector fields\, and how phenomen a unique to small characteristic – such as non-lifting vector fields on rational double point singularities (RDPs) – can be illuminated using th e group-scheme framework.If time permits\, I will outline applications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism groups\, (equivariant) compactifications of the affine plane \, group scheme torsors and their smoothness behavior. X-ALT-DESC:

Group schemes provide a refined notion of symmetry in positiv e characteristic: they detect infinitesimal structure invisible to the dis crete automorphism group. Classical examples such as mu_p or alpha_p equip the trivial topological space with a non-trivial algebraic structure.
In this talk I will explain how this perspective can be used to classify weak and RDP del Pezzo surfaces admitting global vector fields\, and how phenomena unique to small characteristic – such as non-lifting vector fi elds on rational double point singularities (RDPs) – can be illuminated using the group-scheme framework.
If time permits\, I will outline ap plications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism groups\, (equivariant) compactifications of th e affine plane\, group scheme torsors and their smoothness behavior.

DTEND;TZID=Europe/Zurich:20260310T120000 END:VEVENT BEGIN:VEVENT UID:news1987@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260227T105906 DTSTART;TZID=Europe/Zurich:20260303T103000 SUMMARY:Seminar Algebra and Geometry: Alessandra Sarti (Université de Poit iers) DESCRIPTION:Enriques surfaces are special free quotients of K3 surfaces by a fixed point free involution. In higher dimension the notion can be gener alized and one can introduce Enriques manifolds and in the singular settin g\, Log Enriques vaieties. In this talk I will explain general properties of Enriques manifolds and of Log Enriques varieties. I will then provide and discuss several examples in the singular setting\, in particular  I w ill talk about Log Enriques varieties that arise as quotients of generaliz ed Fermat manifolds. These manifolds were studied recently by Hidalgo\, Hu ghes and Leyton-Alvarez. The results that I will present are contained in several joint papers with S. Boissière\, C. Camere\, M. Nieper-Wisskirch en and in a recent work in progress with A. Palomino. X-ALT-DESC:Enriques surfaces are special free quotients of K3 surfaces by a fixed point free involution. In higher dimension the notion can be genera lized and one can introduce Enriques manifolds and in the singular setting \, Log Enriques vaieties. \;In this talk I will explain general proper ties of Enriques manifolds and of Log Enriques varieties. I will then prov ide and discuss several examples in the singular setting\, in particular&n bsp\; I will talk about Log Enriques varieties that arise as quotients of generalized Fermat manifolds. These manifolds were studied recently by Hid algo\, Hughes and Leyton-Alvarez. \;
The results that I will pres ent are contained in several joint papers with S. Boissière\, C. Camere\, M. Nieper-Wisskirchen and in a recent work in progress with A. Palomino. DTEND;TZID=Europe/Zurich:20260303T120000 END:VEVENT BEGIN:VEVENT UID:news1983@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260211T132241 DTSTART;TZID=Europe/Zurich:20260218T150000 SUMMARY:Seminar Algebra and Geometry: Antonio Laface (Universidad de Concep ción) DESCRIPTION:In 1959\, Nagata produced a counterexample to Hilbert’s 14th problem via a linear action of a non-reductive group. The resulting non-fi nitely generated invariant algebra can be interpreted as the Cox ring of a blow-up of P^2 at points\, and in this framework he formulated his conjec ture on plane curves. More recently\, in joint work with Castravet\, Tevel ev and Ugaglia we show that if the blow-up of certain toric surfaces at a general point has a non-polyhedral pseudoeffective cone\, then the pseudoe ffective cone of M̄_{0\,n} is not polyhedral for n ≥ 10. These results motivate a systematic study of Cox rings of blow-ups of toric varieties at a general point.In this talk I focus on minimal toric surfaces\, namely t hose without curves of negative self-intersection. Such surfaces are cycli c quotients of either P^2 or P^1 x P^1. For quotients of P^2\, the blow-up at a general point may fail to be a Mori Dream Space\, for instance when the semiample cone is not closed\, or when the effective cone is not close d. In contrast\, for quotients of P^1 x P^1\, we prove that the blow-up at a general point is always a Mori Dream Space.This is joint work with Luca Ugaglia. X-ALT-DESC:

In 1959\, Nagata produced a counterexample to Hilbert’s 14t h problem via a linear action of a non-reductive group. The resulting non- finitely generated invariant algebra can be interpreted as the Cox ring of a blow-up of P^2 at points\, and in this framework he formulated his conj ecture on plane curves. More recently\, in joint work with Castravet\, Tev elev and Ugaglia we show that if the blow-up of certain toric surfaces at a general point has a non-polyhedral pseudoeffective cone\, then the pseud oeffective cone of M̄_{0\,n} is not polyhedral for n ≥ 10. These result s motivate a systematic study of Cox rings of blow-ups of toric varieties at a general point.

In this talk I focus on minimal toric surfa ces\, namely those without curves of negative self-intersection. Such surf aces are cyclic quotients of either P^2 or P^1 x P^1. For quotients of P^2 \, the blow-up at a general point may fail to be a Mori Dream Space\, for instance when the semiample cone is not closed\, or when the effective con e is not closed. In contrast\, for quotients of P^1 x P^1\, we prove that the blow-up at a general point is always a Mori Dream Space.

Th is is joint work with Luca Ugaglia.

DTEND;TZID=Europe/Zurich:20260218T160000 END:VEVENT BEGIN:VEVENT UID:news1982@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260211T131820 DTSTART;TZID=Europe/Zurich:20260217T103000 SUMMARY:Seminar Algebra and Geometry: Michela Artebani (Universidad de Conc epción) DESCRIPTION:The classification of  Mori dream spaces - equivalently\, norm al projective varieties with finitely generated Cox ring - is closely tied to positivity properties of the anticanonical class. In particular\, tori c and Fano varieties provide fundamental classes of examples with finitely generated Cox rings. In contrast\, Calabi-Yau varieties lie at the bounda ry of positivity: there is no general criterion deciding when they are Mor i dream spaces\, and their birational geometry (and birational automorphis m groups) can be remarkably rich.\\r\\nIn this talk we focus on Calabi--Ya u varieties $X$ arising as  general anticanonical hypersurfaces of smooth toric Fano varieties $Z$. Our results are formulated in terms of primitiv e pairs of the anticanonical polytope of $Z$\, which is a smooth reflexive polytope. We present two complementary theorems. The first result provide s sufficient combinatorial conditions on primitive pairs ensuring that $X$ is a Mori dream space\, and it yields an explicit presentation of the Cox ring $R(X)$ in terms of $R(Z)$  and the defining equation of $X$. The se cond result goes in the opposite direction: the existence of certain relat ions among primitive pairs forces $\\mathrm{Bir}(X)$ to be infinite\, and hence $X$ cannot be a Mori dream space. The proof of the first theorem bui lds on the approach of Herrera-Laface-Ugaglia on Cox rings of embedded var ieties\, while the second generalizes ideas of Kawamata and Ottem for anti canonical hypersurfaces in products of projective spaces. As an applicatio n\, we obtain a complete classification of Mori dream Calabi-Yau hypersurf aces in dimensions $2$ and $3$. In particular\, for these hypersurfaces th ere is a sharp dichotomy:  either $R(X)$ is finitely generated  or $\\ma thrm{Bir}(X)$ is infinite.\\r\\nThis is joint work with Antonio Laface and Luca Ugaglia. X-ALT-DESC:

The classification of  \;Mori dream spaces - equivalently \, normal projective varieties with finitely generated Cox ring - is close ly tied to positivity properties of the anticanonical class. In particular \, toric and Fano varieties provide fundamental classes of examples with f initely generated Cox rings. In contrast\, Calabi-Yau varieties lie at the boundary of positivity: there is no general criterion deciding when they are Mori dream spaces\, and their birational geometry (and birational auto morphism groups) can be remarkably rich.

\n

In this talk we focus on Calabi--Yau varieties $X$ arising as  \;general anticanonical hypersur faces of smooth toric Fano varieties $Z$. Our results are formulated in te rms of primitive pairs of the anticanonical polytope of $Z$\, which is a s mooth reflexive polytope. We present two complementary theorems. The first result provides sufficient combinatorial conditions on primitive pairs en suring that $X$ is a Mori dream space\, and it yields an explicit presenta tion of the Cox ring $R(X)$ in terms of $R(Z)$  \;and the defining equ ation of $X$. The second result goes in the opposite direction: the existe nce of certain relations among primitive pairs forces $\\mathrm{Bir}(X)$ t o be infinite\, and hence $X$ cannot be a Mori dream space. The proof of t he first theorem builds on the approach of Herrera-Laface-Ugaglia on Cox r ings of embedded varieties\, while the second generalizes ideas of Kawamat a and Ottem for anticanonical hypersurfaces in products of projective spac es. As an application\, we obtain a complete classification of Mori dream Calabi-Yau hypersurfaces in dimensions $2$ and $3$. In particular\, for th ese hypersurfaces there is a sharp dichotomy:  \;either $R(X)$ is fini tely generated  \;or $\\mathrm{Bir}(X)$ is infinite.

\n

This is j oint work with Antonio Laface and Luca Ugaglia.

DTEND;TZID=Europe/Zurich:20260217T120000 END:VEVENT BEGIN:VEVENT UID:news1975@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260211T113718 DTSTART;TZID=Europe/Zurich:20260120T103000 SUMMARY:Seminar Algebra and Geometry: Gebhard Martin (Universität Bonn) DESCRIPTION:Salem numbers appear naturally as dynamical degrees of isometri es of hyperbolic lattices and hence in the study of entropy of surface aut omorphisms. The conjecturally smallest Salem number is Lehmer's number $\\ lambda_{10}$\, which can be realized by automorphisms of K3 surfaces and r ational surfaces by work of McMullen. In this talk\, I will explain how to generalize a result of Oguiso asserting the non-realizability of $\\lambd a_{10}$ for automorphisms of Enriques surfaces over the complex numbers to odd characteristics. Then\, I will describe the unique counterexample in characteristic 2. This is joint work with Giacomo Mezzedimi and Davide Ven iani.  X-ALT-DESC:

Salem numbers appear naturally as dynamical degrees of isomet ries of hyperbolic lattices and hence in the study of entropy of surface a utomorphisms. The conjecturally smallest Salem number is Lehmer's number $ \\lambda_{10}$\, which can be realized by automorphisms of K3 surfaces and rational surfaces by work of McMullen. In this talk\, I will explain how to generalize a result of Oguiso asserting the non-realizability of $\\lam bda_{10}$ for automorphisms of Enriques surfaces over the complex numbers to odd characteristics. Then\, I will describe the unique counterexample i n characteristic 2. This is joint work with Giacomo Mezzedimi and Davide V eniani. \;

DTEND;TZID=Europe/Zurich:20260120T120000 END:VEVENT BEGIN:VEVENT UID:news1970@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251214T180559 DTSTART;TZID=Europe/Zurich:20251216T103000 SUMMARY:Seminar Algebra and Geometry: Joseph Malbon (Edinburgh) DESCRIPTION:We describe the automorphism groups of smooth Fano threefolds o f Picard rank 2 and anticanonical degree 28. We then use this to determine which of these threefolds are K-polystable\, and relate the corresponding K-moduli space to a certain GIT-quotient.  X-ALT-DESC:

We describe the automorphism groups of smooth Fano threefolds of Picard rank 2 and anticanonical degree 28. We then use this to determi ne which of these threefolds are K-polystable\, and relate the correspondi ng K-moduli space to a certain GIT-quotient. \;

DTEND;TZID=Europe/Zurich:20251216T120000 END:VEVENT BEGIN:VEVENT UID:news1965@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251206T161101 DTSTART;TZID=Europe/Zurich:20251209T103000 SUMMARY:Seminar Algebra and Geometry: Claudia Stadlmayr (Neuchâtel) DESCRIPTION:Group schemes provide a refined notion of symmetry in positive characteristic: they detect infinitesimal structure invisible to the discr ete automorphism group. Classical examples such as mu_p or alpha_p equip t he trivial topological space with a non-trivial algebraic structure.In thi s talk I will explain how this perspective can be used to classify weak an d RDP del Pezzo surfaces admitting global vector fields\, and how phenomen a unique to small characteristic – such as non-lifting vector fields on rational double point singularities (RDPs) – can be illuminated using th e group-scheme framework.If time permits\, I will outline applications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism groups and (equivariant) compactifications of the affine pla ne. X-ALT-DESC:

Group schemes provide a refined notion of symmetry in positive characteristic: they detect infinitesimal structure invisible to the discrete automorphism group. Classical examples such as mu_p or alpha _p equip the trivial topological space with a non-trivial algebraic struct ure.
In this talk I will explain how this perspectiv e can be used to classify weak and RDP del Pezzo surfaces admitting global vector fields\, and how phenomena unique to small characteristic – such as non-lifting vector fields on rational double point singularities (RDPs ) – can be illuminated using the group-scheme framework.
< strong>If time permits\, I will outline applications and ongoing projects: towards higher-dimensional Fano varieties with infinite automorphism grou ps and (equivariant) compactifications of the affine plane.

DTEND;TZID=Europe/Zurich:20251209T120000 END:VEVENT BEGIN:VEVENT UID:news1957@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251121T102851 DTSTART;TZID=Europe/Zurich:20251125T103000 SUMMARY:Seminar Algebra and Geometry: Gabriel Fazoli (Rennes) DESCRIPTION:A pencil of plane curves determines a foliation on the projecti ve plane which\, generically\, has exactly $d^2$ radial singularities\, an d apart from these singularities\, the foliation is locally given by close d holomorphic 1-forms. In this talk\, we will prove the converse statement : a foliation of degree $2d-2$ on the projective plane with singularities of this type\, under generic conditions\, is determined by a pencil of cur ves. In other words\, every degree $d$ curve passing by the radial singula rities is invariant. In order to do that\, we will introduce the notion of flat partial connections and relate the existence of flat meromorphic ext ensions of a flat partial connections with the existence of invariant curv es. X-ALT-DESC:

A pencil of plane curves determines a foliation on the projec tive plane which\, generically\, has exactly $d^2$ radial singularities\, and apart from these singularities\, the foliation is locally given by clo sed holomorphic 1-forms. In this talk\, we will prove the converse stateme nt: a foliation of degree $2d-2$ on the projective plane with singularitie s of this type\, under generic conditions\, is determined by a pencil of c urves. In other words\, every degree $d$ curve passing by the radial singu larities is invariant. In order to do that\, we will introduce the notion of flat partial connections and relate the existence of flat meromorphic e xtensions of a flat partial connections with the existence of invariant cu rves.

DTEND;TZID=Europe/Zurich:20251125T120000 END:VEVENT BEGIN:VEVENT UID:news1916@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251012T193333 DTSTART;TZID=Europe/Zurich:20251118T103000 SUMMARY:Seminar Algebra and Geometry: Elvira Pérez Callejo (Universidad de Valladolid) DESCRIPTION:In this talk\, we present an algorithmic criterion for determin ing when\, if the foliation is given by polynomials\, it admits a polynom ial first integral whose associated algebraic curve has genus $g\\neq 1$. We explore the restrictions that arise when considering a rational first  integral that is not necessarily polynomial\, how the algorithm works in practice\, and some illustrative examples.\\r\\nThis talk is based on joi nt work with Carlos Galindo and Francisco Monserrat. X-ALT-DESC:

In this talk\, we present an algorithmic criterion for determ ining when\, if the foliation is given by polynomials\, it admits a \; polynomial \;first integral whose associated algebraic curve has genus $g\\neq 1$. We explore the restrictions that arise when considering a rat ional \;first \;integral that is not necessarily polynomial\, how the algorithm works in practice\, and some illustrative examples.

\n

This talk is based on joint work with Carlos Galindo and Francisco Monserr at.

DTEND;TZID=Europe/Zurich:20251118T120000 END:VEVENT BEGIN:VEVENT UID:news1952@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251106T212607 DTSTART;TZID=Europe/Zurich:20251111T103000 SUMMARY:Seminar Algebra and Geometry: Alice Garbagnati (Milano) DESCRIPTION:The K3 surface are one of the two classes of Kähler surfaces w hich are endowed with a symplectic structure. An automorphism α on a K3 s urface X is called symplectic if it preserves this structure and if it has finite order\, the desingularization of the quotient X/α is still a K3 s urface\, a priori different from X.So\, one constructs a relation (the quo tient by an automorphism) between different families of K3 surfaces. The f amilies of projective K3 surfaces admitting a symplectic involution and th e ones of their quotient are intensively studied in the last decades. In t his talk\, I will present the classical known results for the generic memb er of these families and then I consider specializations of some of them. In particular\, I discuss the cases in which the K3 surface admitting the involution and its quotient are contained in the same family\, and/or are isomorphic. The first and most famous example of this phenomenon is the on e in which the symplectic involution is induced by a translation by a 2-to rsion section on an elliptic fibration\, i.e. it is a van Geemen--Sarti in volution. We provide other examples and study specializations of both van Geemen--Sarti involutions and of the other ones presented. X-ALT-DESC:The K3 surface are one of the two classes of Kähler surfaces wh ich are endowed with a symplectic structure. An automorphism α on a K3 su rface X is called symplectic if it preserves this structure and if it has finite order\, the desingularization of the quotient X/α is still a K3 su rface\, a priori different from X.So\, one constructs a relation (the quot ient by an automorphism) between different families of K3 surfaces. The fa milies of projective K3 surfaces admitting a symplectic involution and the ones of their quotient are intensively studied in the last decades. In th is talk\, I will present the classical known results for the generic membe r of these families and then I consider specializations of some of them. I n particular\, I discuss the cases in which the K3 surface admitting the i nvolution and its quotient are contained in the same family\, and/or are i somorphic. The first and most famous example of this phenomenon is the one in which the symplectic involution is induced by a translation by a 2-tor sion section on an elliptic fibration\, i.e. it is a van Geemen--Sarti inv olution. We provide other examples and study specializations of both van G eemen--Sarti involutions and of the other ones presented. DTEND;TZID=Europe/Zurich:20251111T120000 END:VEVENT BEGIN:VEVENT UID:news1940@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251031T202857 DTSTART;TZID=Europe/Zurich:20251104T100000 SUMMARY:Seminar Algebra and Geometry: Crislaine Kuster (Tsinghua University ) DESCRIPTION:I will begin the talk with an introduction to foliations and th e moduli spaces of foliations. I will then discuss the known results on th e problem of describing the space of codimension-one foliations with a fix ed invariant on algebraic varieties. Finally\, I will focus on uniruled va rieties\, define the degree of a codimension-one foliation with respect to a minimal family of rational curves\, and explore the techniques related to deformations of rational curves along foliations. X-ALT-DESC:

I will begin the talk with an introduction to foliations and the moduli spaces of foliations. I will then discuss the known results on the problem of describing the space of codimension-one foliations with a f ixed invariant on algebraic varieties. Finally\, I will focus on uniruled varieties\, define the degree of a codimension-one foliation with respect to a minimal family of rational curves\, and explore the techniques relate d to deformations of rational curves along \;foliations.

DTEND;TZID=Europe/Zurich:20251104T113000 END:VEVENT BEGIN:VEVENT UID:news1930@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251022T170234 DTSTART;TZID=Europe/Zurich:20251028T103000 SUMMARY:Seminar Algebra and Geometry: Anne Schnattinger (Neuchâtel) DESCRIPTION:Given a smooth hyperquadric Y in P^4\, we consider its blowup  X along a smooth irreducible curve C contained in Y. We study the qu estion\, when X is a weak Fano threefold\, that is\, when it has a nef and big anticanonical divisor. We are able to give a complete classifi cation of such threefolds only depending on some geometric properties of C\, particularly its genus and degree. We introduce the main proof idea s which include the analysis of the linear system given by the antican onical divisor of X\, as well as studying curves contained in a smooth K3 surface of degree 6. X-ALT-DESC:

Given \;a smooth hyperquadric \;Y in P^4\, we conside r its blowup \;X along \;a smooth irreducible curve \;C contai ned \;in Y. We study \;the question\, when \;X is \;a weak  \;Fano threefold\, that is\, when it \;has a nef and big anticano nical divisor. We \;are able to give \;a complete \;classifica tion of such threefolds only depending \;on some geometric properties& nbsp\;of C\, particularly its genus \;and degree. We introduce \;t he main proof ideas which include \;the analysis \;of the linear&n bsp\;system given \;by the anticanonical divisor of X\, as well \; as studying curves contained in a smooth K3 surface of degree \;6.

DTEND;TZID=Europe/Zurich:20251028T120000 END:VEVENT BEGIN:VEVENT UID:news1921@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20251012T193216 DTSTART;TZID=Europe/Zurich:20251014T103000 SUMMARY:Seminar Algebra and Geometry: Antoine Pinardin (Universität Basel) DESCRIPTION:We will recall how the classification of the subgroups of Cremo na up to conjugation relies on the study of groups of symmetries of ration al varieties and equivariant birational equivalence. Two questions current ly have a particular interest for researchers. A subgroup G of Cremona is linearizableif it is conjugated to a group of Automorphisms of the project ive space. It is solid if\, after regularization and G-MMP\, it can only a ct on a Fano variety with invariant class group of rank one.\\r\\nWe will give the complete answer to both questions in dimension 2. The answer for linearizability is a joint work with A.Sarikyan and E.Yasinsky. X-ALT-DESC:

We will recall how the classification of the subgroups of Cre mona up to conjugation relies on the study of groups of symmetries of rati onal varieties and equivariant birational equivalence. Two questions curre ntly have a particular interest for researchers. A subgroup G of Cremona i s linearizableif it is conjugated to a group of Automorphisms of the proje ctive space. It is solid if\, after regularization and G-MMP\, it can only act on a Fano variety with invariant class group of rank one.

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We will give the complete answer to both questions in dimension 2. The answer for linearizability is a joint work with A.Sarikyan and E.Yasinsky.

DTEND;TZID=Europe/Zurich:20251014T120000 END:VEVENT BEGIN:VEVENT UID:news1911@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250917T104530 DTSTART;TZID=Europe/Zurich:20250923T103000 SUMMARY:Seminar Algebra and Geometry: Sokratis Zikas (IMPA) DESCRIPTION:In this talk I will present birational maps obtained by blowing up smooth space curves of genus 11 and degree 10. We will completely char acterize the loci in the Hilbert scheme $H_{g\,d}^S$ where the geometry of the birational map changes. We will also examine how varying the curve in $H_{g\,d}^S$ affects the rigidity of the corresponding birational map\, i n the sense of rank 3 fibrations. X-ALT-DESC:

In this talk I will present birational maps obtained by blowi ng up smooth space curves of genus 11 and degree 10. We will completely ch aracterize the loci in the Hilbert scheme $H_{g\,d}^S$ where the geometry of the birational map changes. We will also examine how varying the curve in $H_{g\,d}^S$ affects the rigidity of the corresponding birational map\, in the sense of rank 3 fibrations.

DTEND;TZID=Europe/Zurich:20250923T000000 END:VEVENT BEGIN:VEVENT UID:news1858@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250525T181523 DTSTART;TZID=Europe/Zurich:20250528T160000 SUMMARY:Seminar Algebra and Geometry: Fernando Figueroa (Northwestern Unive rsity) DESCRIPTION:Log Calabi-Yau Pairs are a generalization of Calabi-Yau varieti es\, naturally occurring when considering families or branched covers. The Complexity of a Calabi-Yau pair measures how far it is from being a toric pair. More concretely\,  Brown\, McKernan\, Svaldi and Zong proved that any Calabi-Yau pair of index one and complexity 0 is a toric pair. Recent work of Mauri and Moraga has studied its crepant birational analogue\, the "birational complexity"\, which measures how far the pair is from admitti ng a birational toric model. In this talk we will extend some of the previ ously known results for Calabi-Yau pairs of index one to arbitrary index. In particular we completely characterize Calabi-Yau pairs of complexity ze ro and arbitrary index. This is based on joint work with Joshua Enwright. X-ALT-DESC:

Log Calabi-Yau Pairs are a generalization of Calabi-Yau varie ties\, naturally occurring when considering families or branched covers. The Complexity of a Calabi-Yau pair measures how far it is from being a toric pair. More concretely\, \; Brown\, McKernan\, Svaldi and Zong proved that any Calabi-Yau pair of index one and complexity 0 is a toric pair.
Recent work of Mauri and Moraga has studied its crepant birati onal analogue\, the "birational complexity"\, which measures how far the p air is from admitting a birational toric model.
In this talk we will extend some of the previously known results for Calabi-Yau pairs of index one to arbitrary index. In particular we completely characterize Calabi-Y au pairs of complexity zero and arbitrary index.
This is based on jo int work with Joshua \;Enwright.

DTEND;TZID=Europe/Zurich:20250528T173000 END:VEVENT BEGIN:VEVENT UID:news1843@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250515T093003 DTSTART;TZID=Europe/Zurich:20250520T103000 SUMMARY:Seminar Algebra and Geometry: Francesco Denisi (Université Paris-C ité) DESCRIPTION:Mori dream spaces form a class of algebraic varieties that play a significant role in birational geometry\, as they exhibit ideal behavio ur within the minimal model program. In this talk\, we first motivate and discuss the notion of a Mori dream space\, providing numerous examples and non-examples. We then explore the birational geometry of hypersurfaces in products of weighted projective spaces\, as well as in more general ambie nt spaces\, focusing in particular on cases where such hypersurfaces are M ori dream spaces. We generalise results previously obtained by J.C. Ottem and\, if time permits\, conclude with a few remarks on the Kawamata–Morr ison cone conjecture for certain anticanonical Calabi–Yau hypersurfaces in products of weighted projective spaces. X-ALT-DESC:

Mori dream spaces form a class of algebraic varieties that pl ay a significant role in birational geometry\, as they exhibit ideal behav iour within the minimal model program. In this talk\, we first motivate an d discuss the notion of a Mori dream space\, providing numerous examples a nd non-examples. We then explore the birational geometry of hypersurfaces in products of weighted projective spaces\, as well as in more general amb ient spaces\, focusing in particular on cases where such hypersurfaces are Mori dream spaces. We generalise results previously obtained by J.C. Otte m and\, if time permits\, conclude with a few remarks on the Kawamata–Mo rrison cone conjecture for certain anticanonical Calabi–Yau hypersurface s in products of weighted projective spaces.

DTEND;TZID=Europe/Zurich:20250520T120000 END:VEVENT BEGIN:VEVENT UID:news1877@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250512T093231 DTSTART;TZID=Europe/Zurich:20250514T143000 SUMMARY:Seminar Algebra and Geometry: Sokratis Zikas (IMPA) DESCRIPTION:Mori Dream Spaces are a special kind of varieties introduced by Hu and Keel that enjoy very good properties with respect to the Minimal M odel Program. While Mori Dreamness is a very desirable property\, it is no t very well behaved with respect to even the simplest birational maps: blo wups. In this talk we study Mori Dreamness of blowups along space curves: we provide various sufficient criteria as well obstructions to the blowup being a Mori Dream Space. We also study how this property behaves while va rying the curve in the corresponding Hilbert scheme and show that it is ne ither an open nor a closed condition. Furthermore we exhibit examples of H ilbert schemes whose general element does not give rise to a Mori Dream Sp ace\, while special elements do\, and vice versa. This is joint work in p rogress with Tiago Duarte Guerreiro. X-ALT-DESC:

Mori Dream Spaces are a special kind of varieties introduced by Hu and Keel that enjoy very good properties with respect to the Minimal Model Program. While Mori Dreamness is a very desirable property\, it is not very well behaved with respect to even the simplest birational maps: b lowups. In this talk we study Mori Dreamness of blowups along space curves : we provide various sufficient criteria as well obstructions to the blowu p being a Mori Dream Space. We also study how this property behaves while varying the curve in the corresponding Hilbert scheme and show that it is neither an open nor a closed condition. Furthermore we exhibit examples of Hilbert schemes whose general element does not give rise to a Mori Dream Space\, while special elements do\, and vice versa. \;This is joint wo rk in progress with Tiago Duarte Guerreiro.

DTEND;TZID=Europe/Zurich:20250514T160000 END:VEVENT BEGIN:VEVENT UID:news1862@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250422T171418 DTSTART;TZID=Europe/Zurich:20250513T103000 SUMMARY:Seminar Algebra and Geometry: Pascal Fong (Leibniz Universität Han nover) DESCRIPTION:Recently\, Brion introduced and developed the theory of equivar iantly normal curves. These curves arise naturally in the study of smooth projective surfaces equipped with a faithful action of an elliptic curve. We will see that such a surface is isomorphic to a contracted product E\\t imes^G X\, where E is an elliptic curve\, G is a finite subgroup scheme of E and X is a G-normal curve. In this talk\, we study this family of surfa ces\, which contains the classical example of quasi-hyperelliptic surfaces given by Bombieri and Mumford. X-ALT-DESC:

Recently\, Brion introduced and developed the theory of equiv ariantly normal curves. These curves arise naturally in the study of smoot h projective surfaces equipped with a faithful action of an elliptic curve . We will see that such a surface is isomorphic to a contracted product E\ \times^G X\, where E is an elliptic curve\, G is a finite subgroup scheme of E and X is a G-normal curve. In this talk\, we study this family of sur faces\, which contains the classical example of quasi-hyperelliptic surfac es given by Bombieri and Mumford.

DTEND;TZID=Europe/Zurich:20250513T120000 END:VEVENT BEGIN:VEVENT UID:news1845@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250402T112840 DTSTART;TZID=Europe/Zurich:20250429T103000 SUMMARY:Seminar Algebra and Geometry: Nikolaos Tsakanikas (EPFL) DESCRIPTION:In this talk\, which is based on joint work with Denisi\, Ortiz and Xie\, I will introduce the class of primitive Enriques varieties. I w ill discuss the basic properties of these objects\, showing in particular that the smooth ones are Enriques manifolds\, and I will also present some examples of (singular) primitive Enriques varieties. Finally\, I will ske tch the proof of the following termination statement: if X is an Enriques manifold and B is an R-divisor on X such that the pair (X\,B) is log canon ical\, then any (K_X+B)-MMP terminates. X-ALT-DESC:

In this talk\, which is based on joint work with Denisi\, Ortiz and Xie\, I will introduce the class of primitive Enri ques varieties. I will discuss the basic properties of these objects\, sho wing in particular that the smooth ones are Enriques manifolds\, and I wil l also present some examples of (singular) primitive Enriques varieties. F inally\, I will sketch the proof of the following termination statement: i f X is an Enriques manifold and B is an R-divisor on X such that the pair (X\,B) is log canonical\, then any (K_X+B)-MMP terminates.

DTEND;TZID=Europe/Zurich:20250429T120000 END:VEVENT BEGIN:VEVENT UID:news1857@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250410T103510 DTSTART;TZID=Europe/Zurich:20250415T103000 SUMMARY:Seminar Algebra and Geometry: Aline Zanardini (EPFL) DESCRIPTION:In this talk\, we will consider the problem of classifying line ar systems of hypersurfaces inside projective space and up to projective e quivalence. I will report on a possible approach to solving this problem v ia geometric invariant theory\, and I will further illustrate how such an approach can be applied to some relevant geometric examples.\\r\\nThis is based on joint work with Masafumi Hattori. X-ALT-DESC:

In this talk\, we will consider the problem of classifying li near systems of hypersurfaces inside projective space and up to projective equivalence. I will report on a possible approach to solving this problem via geometric invariant theory\, and I will further illustrate how such a n approach can be applied to some relevant geometric examples.

\n

Thi s is based on joint work with Masafumi Hattori.

DTEND;TZID=Europe/Zurich:20250415T120000 END:VEVENT BEGIN:VEVENT UID:news1844@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250402T104121 DTSTART;TZID=Europe/Zurich:20250408T163000 SUMMARY:Seminar Algebra and Geometry: Livia Campo (University of Vienna) DESCRIPTION:The existence of Kaehler-Einstein metrics on Fano 3-folds can b e determined by studying lower bounds of stability thresholds. An effectiv e way to verify such bounds is to construct flags of point-curve-surface i nside the Fano 3-folds. This approach was initiated by Abban-Zhuang\, and allows us to restrict the computation of bounds for stability thresholds o nly on flags. We employ this machinery to prove K-stability of terminal qu asi-smooth Fano 3-fold hypersurfaces. This is deeply intertwined with the geometry of the hypersurfaces: in fact\, birational rigidity and superrigi dity play a crucial role. The superrigid case had been attacked by Kim-Oka da-Won. In this talk I will discuss the K-stability of strictly rigid Fano hypersurfaces via Abban-Zhuang Theory. This is a joint work with Takuzo O kada. X-ALT-DESC:

The existence of Kaehler-Einstein metrics on Fano 3-folds can be determined by studying lower bounds of stability thresholds. An effect ive way to verify such bounds is to construct flags of point-curve-surface inside the Fano 3-folds. This approach was initiated by Abban-Zhuang\, an d allows us to restrict the computation of bounds for stability thresholds only on flags. We employ this machinery to prove K-stability of terminal quasi-smooth Fano 3-fold hypersurfaces. This is deeply intertwined with th e geometry of the hypersurfaces: in fact\, birational rigidity and superri gidity play a crucial role. The superrigid case had been attacked by Kim-O kada-Won. In this talk I will discuss the K-stability of strictly rigid Fa no hypersurfaces via Abban-Zhuang Theory. This is a joint work with Takuzo Okada.

\n\n DTEND;TZID=Europe/Zurich:20250408T180000 END:VEVENT BEGIN:VEVENT UID:news1855@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250407T154329 DTSTART;TZID=Europe/Zurich:20250408T103000 SUMMARY:Seminar Algebra and Geometry: Daniela Paiva (IMPA) DESCRIPTION:The problem of determining which automorphisms of a projective K3 surface S are induced by birational maps of an ambient space in which i t is embedded remains open. This is known as Gizatullin’s problem. In th is seminar\, I will provide a general background on the theory of K3 surfa ces and the birational geometry of Fano 3-folds\, and explain how the inte rplay between these areas can be exploited to address the problem. In part icular\, I will present a solution to Gizatullin’s problem in certain sp ecific cases. The results I will present are part of joint work with Carol ina Araujo\, Michela Artebani\, Alice Garbagnati\, Ana Quedo\, and Sokrati s Zikas. X-ALT-DESC:

The problem of determining which automorphisms of a projectiv e K3 surface S are induced by birational maps of an ambient space in which it is embedded remains open. This is known as Gizatullin’s problem.
In this seminar\, I will provide a general background on the theory of K3 surfaces and the birational geometry of Fano 3-folds\, and explain how the interplay between these areas can be exploited to address the problem. In particular\, I will present a solution to Gizatullin’s problem in ce rtain specific cases.
The results I will present are part of joint w ork with Carolina Araujo\, Michela Artebani\, Alice Garbagnati\, Ana Quedo \, and Sokratis Zikas.

DTEND;TZID=Europe/Zurich:20250408T120000 END:VEVENT BEGIN:VEVENT UID:news1854@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20250402T112935 DTSTART;TZID=Europe/Zurich:20250401T103000 SUMMARY:Seminar Algebra and Geometry: Antoine Pinardin (University of Edinb urgh) DESCRIPTION:The G-Fano varieties are the varieties whose anticanonical div isor is ample\, and whose invariant part of the Picard group has rank one. In the classification of finite subgroups of Cremona up to conjugation\,  G-Fano varieties play a fundamental role\, analogous to the way finite g roups are constructed through successive extensions by simple groups. If a G-Fano variety only admits equivariant birational maps to other G-Fano va rieties\, it is called G-solid. Roughly speaking\, this means that the gro up G is not induced by actions on lower dimensional Fano varieties.\\r\\nI n this talk\, I will present the complete answer I gave to the G-solidity problem for surfaces over the field of complex numbers\, and some results achieved for threefolds in an ongoing project with Zhijia Zhang. X-ALT-DESC:

The \;G-Fano varieties are the varieties whose anticanoni cal divisor is ample\, and whose invariant part of the Picard group has ra nk one. In the classification of finite subgroups of Cremona up to conjuga tion\, \;G-Fano varieties play a fundamental role\, analogous to the w ay finite groups are constructed through successive extensions by simple g roups. If a G-Fano variety only admits equivariant birational maps to othe r G-Fano varieties\, it is called G-solid. Roughly speaking\, this means t hat the group G is not induced by actions on lower dimensional Fano variet ies.

\n

In this talk\, I will present the complete answer I gave to t he G-solidity problem for surfaces over the field of complex numbers\, and some results achieved for threefolds in an ongoing project with Zhijia Zh ang.

DTEND;TZID=Europe/Zurich:20250401T120000 END:VEVENT BEGIN:VEVENT UID:news1023@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20200220T145956 DTSTART;TZID=Europe/Zurich:20200225T103000 SUMMARY:Seminar Algebra and Geometry: Anne Lonjou (Universität Basel) DESCRIPTION:A key tool to study the plane Cremona group is its action on a hyperbolic space. Saddly\, in higher rank such an action is not available. Recently in geometric group theory\, actions on CAT(0) cube complexes tur ned out to be a powerfull tool to study a large class of groups.    \\r \\nIn this talk\, based on a common work with Christian Urech\, we will co nstruct such complexes on which Cremona groups of rank n act. We will then see which kind of results on these groups we can obtain. X-ALT-DESC:

A key tool to study the plane Cremona group is its action on a hyperbolic space. Saddly\, in higher rank such an action is not availabl e. Recently in geometric group theory\, actions on CAT(0) cube complexes t urned out to be a powerfull tool to study a large class of groups. \;  \; \;

\n

In this talk\, based on a common work with Christia n Urech\, we will construct such complexes on which Cremona groups of rank n act. We will then see which kind of results on these groups we can obta in.

DTEND;TZID=Europe/Zurich:20200225T120000 END:VEVENT BEGIN:VEVENT UID:news987@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191206T022316 DTSTART;TZID=Europe/Zurich:20191209T150000 SUMMARY:Seminar Algebra and Geometry: Michel van Garrel (Warwick) DESCRIPTION:In this joint work with Christian Böhning and Hans-Christian von Bothmer we apply Voisin's criterion of existence of a decomposition o f the diagonal to semistable degenerations. In doing so\, we obtain partia l results towards proving that very general cubic threefolds are stably ir rational. X-ALT-DESC:In this joint work with Christian \;Böhning \;and Hans- Christian von Bothmer we apply Voisin's criterion of existence of a decomp osition of the diagonal to semistable degenerations. In doing so\, we obta in partial results towards proving that very general cubic threefolds are stably irrational. DTEND;TZID=Europe/Zurich:20191209T163000 END:VEVENT BEGIN:VEVENT UID:news922@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191127T114131 DTSTART;TZID=Europe/Zurich:20191203T103000 SUMMARY:Seminar Algebra and Geometry: Erik Paemurru (University of Loughbor ough) DESCRIPTION:It is known that quasismooth 3-fold Fano hypersurfaces with ind ex 1 in weighted projective spaces over ℂ are birationally rigid (not bi rational to any other Fano 3-folds\, conic bundles or del Pezzo fibrations ). But very little is known when they carry non-orbifold singularities. I consider sextic double solids\, one of the simplest such 3-folds\, which h ave an isolated cA_n singularity. I have shown that n is at most 8\, and t hat rigidity fails for n > 3. In this talk\, I will illustrate this phenom enon by giving some examples. X-ALT-DESC:It is known that quasismooth 3-fold Fano hypersurfaces with inde x 1 in weighted projective spaces over ℂ are birationally rigid (not bir ational to any other Fano 3-folds\, conic bundles or del Pezzo fibrations) . But very little is known when they carry non-orbifold singularities. I c onsider sextic double solids\, one of the simplest such 3-folds\, which ha ve an isolated cA_n singularity. I have shown that n is at most 8\, and th at rigidity fails for n >\; 3. In this talk\, I will illustrate this phe nomenon by giving some examples. DTEND;TZID=Europe/Zurich:20191203T120000 END:VEVENT BEGIN:VEVENT UID:news924@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191112T123824 DTSTART;TZID=Europe/Zurich:20191126T103000 SUMMARY:Seminar Algebra and Geometry: Carlos Amendola (University of Munich ) DESCRIPTION:We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all 2-dimensional Gorenstein toric Fano varieties. We show tha t the ML degree is equal to the degree of the surface in every case except for the quintic del Pezzo surface with two singular points of type A1 and provide explicit expressions that allow to compute the maximum likelihood estimate in closed form whenever the ML degree is less than 5. We then ex plore the reasons for the ML degree drop using A-discriminants and interse ction theory. Based on joint work with Dimitra Kosta and Kaie Kubjas. X-ALT-DESC:We study the maximum likelihood estimation problem for several c lasses of toric Fano models. We start by exploring the maximum likelihood degree for all 2-dimensional Gorenstein toric Fano varieties. We show that the ML degree is equal to the degree of the surface in every case except for the quintic del Pezzo surface with two singular points of type A1 and provide explicit expressions that allow to compute the maximum likelihood estimate in closed form whenever the ML degree is less than 5. We then exp lore the reasons for the ML degree drop using A-discriminants and intersec tion theory. Based \;on joint work with Dimitra Kosta and Kaie Kubjas. DTEND;TZID=Europe/Zurich:20191126T120000 END:VEVENT BEGIN:VEVENT UID:news927@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191104T113358 DTSTART;TZID=Europe/Zurich:20191112T103000 SUMMARY:Seminar Algebra and Geometry: Enrica Mazzon (Imperial College) DESCRIPTION:To a degeneration of varieties\, we can associate the dual inte rsection complex\, a topological space that encodes the combinatoric of th e central fiber and reflects the geometry of the generic fiber. The points of the dual complex can be identified to valuations on the function field of the variety\, hence the dual complex can be embedded in the Berkovich space of the variety.In this talk I will explain how this interpretation g ives an insight in the study of the dual complexes. I will focus on some d egenerations of hyper-Kähler varieties and show that we are able to deter mine the homeomorphism type of their dual complex using techniques of Berk ovich geometry. The results are in accordance with the predictions of mirr or symmetry\, and the recent work about the rational homology of dual comp lexes of degenerations of hyper-Kähler varieties\, due to Kollár\, Laza\ , Saccà and Voisin.This is joint work with Morgan Brown. X-ALT-DESC:To a degeneration of varieties\, we can associate the dual inter section complex\, a topological space that encodes the combinatoric of the central fiber and reflects the geometry of the generic fiber. The points of the dual complex can be identified to valuations on the function field of the variety\, hence the dual complex can be embedded in the Berkovich s pace of the variety.In this talk I will explain how this interpretation gi ves an insight in the study of the dual complexes. I will focus on some de generations of hyper-Kähler varieties and show that we are able to determ ine the homeomorphism type of their dual complex using techniques of Berko vich geometry. The results are in accordance with the predictions of mirro r symmetry\, and the recent work about the rational homology of dual compl exes of degenerations of hyper-Kähler varieties\, due to Kollár\, Laza\, Saccà and Voisin.This is joint work with Morgan Brown.
DTEND;TZID=Europe/Zurich:20191112T120000 END:VEVENT BEGIN:VEVENT UID:news925@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191020T194626 DTSTART;TZID=Europe/Zurich:20191105T103000 SUMMARY:Seminar Algebra and Geometry: Shengyuan Zhao (University of Rennes) DESCRIPTION:Let Y be a smooth complex projective surface. Let U be a connec ted Euclidean open set of Y. Let G be a subgroup of Bir(Y) which acts by h olomorphic diffeomorphisms on U (i.e. preserves U and without indeterminac y points in U)\, in a free\, properly discontinuous and cocompact way\, so that the quotient X=U/G is a compact complex surface. Such a birational t ransformation group G\, or more precisely such a quadruple (Y\,U\,G\,X)\, will be called a birational Kleinian group. Once we have a birational Klei nian group\, the quotient surface is equipped with a birational structure\ , i.e. an atlas of local charts with rational changes of coordinates. I wi ll present some basic properties and subtleties of birational structures\, compared to the classical geometric structures. Then I will begin by stud ying birational structures on a special type of non-algebraic surfaces\, t he Inoue surfaces\, to reveal some of the general strategy. Using classifi cation of solvable and abelian groups of the Cremona group\, and by relati ng the foliations on Inoue surfaces with some birational dynamical systems via Ahlfors-Nevanlinna currents\, I will show that the Inoue surfaces hav e one unique birational structure. Then I will move on to the general stud y of birational Kleinian groups with the additional hypothesis that the qu otient surface is projective. I will explain how to use powerful results f rom Cremona groups\, holomorphic foliations and non-abelian Hodge theory t o get an almost complete classification of such birational Kleinian groups .  X-ALT-DESC:Let Y be a smooth complex projective surface. Let U be a conn ected Euclidean open set of Y. Let G be a subgroup of Bir(Y) which acts by holomorphic diffeomorphisms on U (i.e. preserves U and without indetermin acy points in U)\, in a free\, properly discontinuous and cocompact way\, so that the quotient X=U/G is a compact complex surface. Such a birational transformation group G\, or more precisely such a quadruple (Y\,U\,G\,X)\ , will be called a birational Kleinian group. Once we have a birational Kl einian group\, the quotient surface is equipped with a birational structur e\, i.e. an atlas of local charts with rational changes of coordinates. I will present some basic properties and subtleties of birational structures \, compared to the classical geometric structures. Then I will begin by st udying birational structures on a special type of non-algebraic surfaces\, the Inoue surfaces\, to reveal some of the general strategy. Using classi fication of solvable and abelian groups of the Cremona group\, and by rela ting the foliations on Inoue surfaces with some birational dynamical syste ms via Ahlfors-Nevanlinna currents\, I will show that the Inoue surfaces h ave one unique birational structure. Then I will move on to the general st udy of birational Kleinian groups with the additional hypothesis that the quotient surface is projective. I will explain how to use powerful results from Cremona groups\, holomorphic foliations and non-abelian Hodge theory to get an almost complete classification of such birational Kleinian grou ps. \; DTEND;TZID=Europe/Zurich:20191105T120000 END:VEVENT BEGIN:VEVENT UID:news923@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191004T195327 DTSTART;TZID=Europe/Zurich:20191029T103000 SUMMARY:Seminar Algebra and Geometry: Stavros Papadakis (University of Ioan nina) DESCRIPTION:Un projection theory\, initiated by Miles Reid\, aims to constr uct and analyze complicated commutative rings in terms of simpler ones. It can also be considered as an algebraic language for birational geometry. \\r\\nThe main purpose of the talk is to give a short introduction to the theory and describe some of its applications. X-ALT-DESC:Un projection theory\, initiated by Miles Reid\, aims to constru ct and analyze complicated commutative rings in terms of simpler ones. It can also be considered as an algebraic language for birational geometry. \ nThe main purpose of the talk is to give a short introduction to the theor y and describe some of its applications. DTEND;TZID=Europe/Zurich:20191029T120000 END:VEVENT BEGIN:VEVENT UID:news934@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191004T195339 DTSTART;TZID=Europe/Zurich:20191015T103000 SUMMARY:Seminar Algebra and Geometry: Tomasz Pełka (University of Bern) DESCRIPTION:ℚ-homology planes satisfying the Negativity Conjecture X-ALT-DESC:ℚ-homology planes satisfying the Negativity Conjecture DTEND;TZID=Europe/Zurich:20191015T120000 END:VEVENT BEGIN:VEVENT UID:news933@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20191004T195349 DTSTART;TZID=Europe/Zurich:20191008T103000 SUMMARY:Seminar Algebra and Geometry: Christian Urech (EPFL) DESCRIPTION:Julie Déserti showed that every automorphism of the plane Crem ona group is inner up to a field automorphism of the base-field. In this t alk we generalize this result to Cremona groups of arbitrary rank\, howeve r\, only under the additional restriction that the automorphisms are also homeomorphisms with respect to the Zariski or the Euclidean topology on th e Cremona group. We will consider similar questions for groups of polynomi al automorphisms and groups of birational diffeomorphisms. This is joint w ork with Susanna Zimmermann. X-ALT-DESC: Julie Déserti showed that every automorphism of the plane Crem ona group is inner up to a field automorphism of the base-field. In this t alk we generalize this result to Cremona groups of arbitrary rank\, howeve r\, only under the additional restriction that the automorphisms are also homeomorphisms with respect to the Zariski or the Euclidean topology on th e Cremona group. We will consider similar questions for groups of polynomi al automorphisms and groups of birational diffeomorphisms. This is joint w ork with Susanna Zimmermann. DTEND;TZID=Europe/Zurich:20191008T120000 END:VEVENT BEGIN:VEVENT UID:news898@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190619T152715 DTSTART;TZID=Europe/Zurich:20190703T103000 SUMMARY:Seminar Algebra and Geometry: Stéphane Lamy (Université de Toulou se) DESCRIPTION:The group of tame polynomial automorphisms of the n-dimensional complex affine space is the group generated by linear maps and polynomial transvections. I will describe an action of this group on a metric space whose construction is inspired from the theory of affine Bruhat-Tits build ings. In dimension n = 3\, we show that this space is simply connected wit h non-positive curvature. This allows to get a description of the finite s ubgroups of the 3-dimensional tame group. (Joint work with P. Przytycki) X-ALT-DESC:The group of tame polynomial automorphisms of the n-dimensional complex affine space is the group generated by linear maps and polynomial transvections. I will describe an action of this group on a metric space w hose construction is inspired from the theory of affine Bruhat-Tits buildi ngs. In dimension n = 3\, we show that this space is simply connected with non-positive curvature. This allows to get a description of the finite su bgroups of the 3-dimensional tame group. (Joint work with P. Przytycki) DTEND;TZID=Europe/Zurich:20190703T120000 END:VEVENT BEGIN:VEVENT UID:news883@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190517T143050 DTSTART;TZID=Europe/Zurich:20190521T103000 SUMMARY:Seminar Algebra and Geometry: Prof. Niko Beerenwinkel (Dept. of Bio systems Science and Engineering\, ETHZ) DESCRIPTION:TBA X-ALT-DESC:TBA DTEND;TZID=Europe/Zurich:20190521T120000 END:VEVENT BEGIN:VEVENT UID:news852@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190423T201701 DTSTART;TZID=Europe/Zurich:20190514T103000 SUMMARY:Seminar Algebra and Geometry: Urban Jezernik (University of the Bas que Country) DESCRIPTION:The rationality problem in algebraic geometry asks whether a gi ven variety is birational to a projective space. We will gently introduce the problem and take a look at some recent advances\, principally in the d irection of negative examples constructed via cohomological obstructions. Special focus will be set on quotient varieties by linear group actions. X-ALT-DESC:The rationality problem in algebraic geometry asks whether a giv en variety is birational to a projective space. We will gently introduce t he problem and take a look at some recent advances\, principally in the di rection of negative examples constructed via cohomological obstructions. S pecial focus will be set on quotient varieties by linear group actions. DTEND;TZID=Europe/Zurich:20190514T120000 END:VEVENT BEGIN:VEVENT UID:news846@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190430T141302 DTSTART;TZID=Europe/Zurich:20190507T103000 SUMMARY:Seminar Algebra and Geometry: Yuri Prokhorov (Steklov Mathematical Institute\, Moscow) DESCRIPTION:A conic bundle f: X\\to S is a flat morphism of smooth varietie s whose  fibers are plane conics.  In this talk\, I will first discuss application of  Sarkisov program to the rationality problem of algebraic varieties having conic bundle structures. Then I concentrate on some spec ial\, so-called  tetragonal types of conic bundles\, which lie on the " boundary" between birationally rigid and non-rigid ones and are especiall y interesting for this reason.  The second part of the talk is based on the joint work in progress with V. Shokurov. X-ALT-DESC:A conic bundle f: X\\to S is a flat morphism of smooth varieties whose \; fibers are plane conics. \; \;
In this talk\, I will first discuss application of \; Sarkisov program to the rational ity problem of algebraic varieties having conic bundle structures. \;< br />Then I concentrate on some special\, so-called \; \;tetragonal \;types of conic bundles\, which lie on the "\;bou ndary"\; between birationally rigid and non-rigid ones \;and are e specially interesting for this reason. \; \;
The second part of the talk is based on the joint work \;in progress with V. Shokurov. DTEND;TZID=Europe/Zurich:20190507T120000 END:VEVENT BEGIN:VEVENT UID:news845@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190327T160809 DTSTART;TZID=Europe/Zurich:20190416T103000 SUMMARY:Seminar Algebra and Geometry: Matilde Manzaroli (École Polytechniq ue and Université de Nantes) DESCRIPTION:The study of the topology of real algebraic varieties dates bac k to the work of Harnack\, Klein and Hilbert in the 19th century\; in part icular\, the isotopy type classification of real algebraic curves with a f ixed degree in the real projective plane is a classical subject that has u ndergone considerable evolution. On the other hand\, apart from studies co ncerning Hirzebruch surfaces and at most degree 3 surfaces in the real pro jective space\, not much is known for more general ambient surfaces. In pa rticular\, this is because varieties constructed using the patchworking me thod are hypersurfaces of toric varieties. However\, there are many other real algebraic surfaces. Among these are the real rational surfaces\, and more particularly the real minimal surfaces. In this talk\, we present som e results about the classification of topological types realized by real a lgebraic curves in real minimal del Pezzo surfaces of degree. X-ALT-DESC:The study of the topology of real algebraic varieties dates back to the work of Harnack\, Klein and Hilbert in the 19th century\; in parti cular\, the isotopy type classification of real algebraic curves with a fi xed degree in the real projective plane is a classical subject that has un dergone considerable evolution. On the other hand\, apart from studies con cerning Hirzebruch surfaces and at most degree 3 surfaces in the real proj ective space\, not much is known for more general ambient surfaces. In par ticular\, this is because varieties constructed using the patchworking met hod are hypersurfaces of toric varieties. However\, there are many other r eal algebraic surfaces. Among these are the real rational surfaces\, and m ore particularly the real minimal surfaces. In this talk\, we present some results about the classification of topological types realized by real al gebraic curves in real minimal del Pezzo surfaces of degree. DTEND;TZID=Europe/Zurich:20190416T120000 END:VEVENT BEGIN:VEVENT UID:news637@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190314T120420 DTSTART;TZID=Europe/Zurich:20190319T103000 SUMMARY:Seminar Algebra and Geometry: Mirko Mauri (Imperial College London) DESCRIPTION:The geometric P=W conjecture is a conjectural description of th e asymptotic behavior of a celebrated correspondence in non-abelian Hodge  theory. In particular\, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint wo rk with Enrica Mazzon and Matthew Stevenson\, we manage to compute the fi rst non-trivial examples of dual complexes in the compact case. This requ ires to develop a new theory of essential skeletons over a trivially-value d field. As a byproduct\, inspired by these constructions\, we show that certain character varieties appear in degenerations of compact hyper-Kä hler manifolds.  In this talk we will explain how these new non-archime dean techniques can shed new light into classical algebraic geometry prob lems.  X-ALT-DESC:The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge&n bsp\;theory. In particular\, it is expected \;that the dual boundary&n bsp\;complex of the compactification of character varieties \;is a sph ere. In a joint work with Enrica Mazzon and Matthew Stevenson\, we manage to compute \;the first non-trivial \;examples of dual complexes in the compact case. This requires to develop a new theory of essential skel etons over a trivially-valued field. \;As a byproduct\, inspired by th ese constructions\, we show \;that certain character varieties appear in \;degenerations of compact hyper-Kähler manifolds. \; \;In this talk we will explain how these new \;non-archimedean techniques& nbsp\;can shed new light into classical algebraic geometry problems. \ ; DTEND;TZID=Europe/Zurich:20190319T120000 END:VEVENT BEGIN:VEVENT UID:news821@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190222T141344 DTSTART;TZID=Europe/Zurich:20190305T103000 SUMMARY:Seminar Algebra and Geometry: Federico Lo Bianco (Université de Ma rseille) DESCRIPTION:We consider a holomorphic (singular) foliation F on a projectiv e manifold X and a group G of birational transformations of X which preser ve F (i.e. it permutes the set of leaves). We say that the transverse acti on of G is finite if some finite index subgroup of G fixes each leaf of F. \\r\\nI will briefly recall a criterion for the finiteness of the transve rse action in the case of algebraically integrable foliations (i.e. foliat ions whose leaves coincide with the fibres of a fibration). Then I will ex plain how the presence of certain transverse structures on the foliation a llow to recover the same result\; in this case\, one can study the monodro my of such a structure (which is defined in an analogous way as that of a more familiar (G\,X)-structure) and apply factorization results in order t o reduce the problem to subvarieties of quotients of the product of unit d iscs\, whose geometry is now quite well understood. X-ALT-DESC:We consider a holomorphic (singular) foliation F on a projective manifold X and a group G of birational transformations of X which preserv e F (i.e. it permutes the set of leaves). We say that the transverse actio n of G is finite if some finite index subgroup of G fixes each leaf of F. \nI will briefly recall a criterion for the finiteness of the transverse a ction in the case of algebraically integrable foliations (i.e. foliations whose leaves coincide with the fibres of a fibration). Then I will explain how the presence of certain transverse structures on the foliation allow to recover the same result\; in this case\, one can study the monodromy of such a structure (which is defined in an analogous way as that of a more familiar (G\,X)-structure) and apply factorization results in order to red uce the problem to subvarieties of quotients of the product of unit discs\ , whose geometry is now quite well understood. DTEND;TZID=Europe/Zurich:20190305T120000 END:VEVENT BEGIN:VEVENT UID:news410@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181211T103000 SUMMARY:Seminar Algebra and Geometry: Luca Studer (University of Bern) DESCRIPTION:In the talk we discuss how Oka theory helps to solve systems of equations with complex analytic entries. A classical example is the fact that for every pair of complex analytic functions a\, b: C^n -> C with no common zero there are complex analytic functions x\, y: C^n -> C satisfyin g the Bézout identity ax+by=1. A more recent example is Leiterer's work\, where the solvability of xax^{-1}=b for complex analytic matrix-valued ma ps a\, b: C^n -> Mat(n x n\, C) is investigated. Both examples are brought into the context of the speakers research. X-ALT-DESC:In the talk we discuss how Oka theory helps to solve systems of equations with complex analytic entries. A classical example is the fact t hat for every pair of complex analytic functions a\, b: C^n ->\; C with no common zero there are complex analytic functions x\, y: C^n ->\; C sa tisfying the Bézout identity ax+by=1. A more recent example is Leiterer's work\, where the solvability of xax^{-1}=b for complex analytic matrix-va lued maps a\, b: C^n ->\; Mat(n x n\, C) is investigated. Both examples are brought into the context of the speakers research. DTEND;TZID=Europe/Zurich:20181211T120000 END:VEVENT BEGIN:VEVENT UID:news348@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T083213 DTSTART;TZID=Europe/Zurich:20181204T103000 SUMMARY:Seminar Algebra and Geometry: Bruno Laurent (Grenoble) DESCRIPTION:The varieties which are homogeneous under the action of an alge braic group are very symmetric objects. More generally\, we get a much wid er class of objects\, having a very rich geometry\, by allowing the variet ies to have not a unique orbit\, but a dense orbit. Such varieties are sai d to be almost homogeneous\; this includes the case of toric varities\, wh en the group is an algebraic torus.In this talk\, I will explain how to cl assify the pairs (X\,G) where X is a curve or a surface and G is a smo oth and connected algebraic group acting on X with a dense orbit.For cur ves\, I will mainly focus on the regular ones\, defined over an arbitrary field. Over an algebraically closed field\, the "natural" notion of non-si ngularity is "smoothness". However\, over an arbitrary field\, the weaker notion of "regularity" is more suitable. I will recall the difference betw een those two notions and show that there exist regular homogeneous curves which are not smooth.For surfaces\, I will restrict to the smooth ones\, defined over an algebraically closed field. The situation is more complica ted than for curves. Moreover\, new phenomena and several difficulties app ear in positive characteristic\, and I will highlight them. X-ALT-DESC:The varieties which are homogeneous under the action of an algeb raic group are very symmetric objects. More generally\, we get a much wide r class of objects\, having a very rich geometry\, by allowing the varieti es to have not a unique orbit\, but a dense orbit. Such varieties are said to be almost homogeneous\; this includes the case of toric varities\, whe n the group is an algebraic torus.

In this talk\, I will explai n how to classify the pairs (X\,G) where \;X \;is a curve or a sur face and \;G \;is a smooth and connected algebraic group acting on  \;X \;with a dense orbit.

For curves\, I will mainly f ocus on the regular ones\, defined over an arbitrary field. Over an algebr aically closed field\, the "\;natural"\; notion of non-singularity is "\;smoothness"\;. However\, over an arbitrary field\, the weak er notion of "\;regularity"\; is more suitable. I will recall the difference between those two notions and show that there exist regular hom ogeneous curves which are not smooth.

For surfaces\, I will res trict to the smooth ones\, defined over an algebraically closed field. The situation is more complicated than for curves. Moreover\, new phenomena a nd several difficulties appear in positive characteristic\, and I will hig hlight them. DTEND;TZID=Europe/Zurich:20181204T120000 END:VEVENT BEGIN:VEVENT UID:news341@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181120T103000 SUMMARY:Seminar Algebra and Geometry: Nikon Kurnosov (University of Georgia \, Athens\, US) DESCRIPTION:Hyperkähler manifolds are higher-dimensional generalizations o f K3 surfaces. The Beauville conjecture predicts that the number of deform ation types of compact irreducible hyperkähler manifolds is finite in any dimension. In this talk I will briefly discuss some basic notions of the theory\, explain why hyperkähler manifolds play a very important role in classification of complex manifolds\, and then explain what are the eviden ces for Beauville's conjecture. X-ALT-DESC:Hyperkähler manifolds are higher-dimensional generalizations of K3 surfaces. The Beauville conjecture predicts that the number of deforma tion types of compact irreducible hyperkähler manifolds is finite in any dimension. In this talk I will briefly discuss some basic notions of the t heory\, explain why hyperkähler manifolds play a very important role in c lassification of complex manifolds\, and then explain what are the evidenc es for Beauville's conjecture. DTEND;TZID=Europe/Zurich:20181120T120000 END:VEVENT BEGIN:VEVENT UID:news361@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181113T103000 SUMMARY:Seminar Algebra and Geometry: Lukas Lewark (University of Bern) DESCRIPTION:This talk will explore different notions of positivity of knots \, how to encode such knots as graphs\, and how to unknot them. Joint resu lts with Baader/Liechti and Feller/Lobb will make appearances. No prerequi sites in knot theory will be necessary. X-ALT-DESC:This talk will explore different notions of positivity of knots\ , how to encode such knots as graphs\, and how to unknot them. Joint resul ts with Baader/Liechti and Feller/Lobb will make appearances. No prerequis ites in knot theory will be necessary. DTEND;TZID=Europe/Zurich:20181113T120000 END:VEVENT BEGIN:VEVENT UID:news340@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181106T103000 SUMMARY:Seminar Algebra and Geometry: Juliette Bavard (University of Rennes ) DESCRIPTION:The plane minus a Cantor set and its mapping class group appear in many dynamical contexts\, including group actions on surfaces\, the study of groups of homeomorphisms on a Cantor set\, and complex dynamics.  In this talk\, I will motivate the study of this 'big mapping class grou ps'. I will then present the 'ray graph'\, which is a Gromov-hyperbolic  graph on which this group acts by isometries.   X-ALT-DESC:The plane minus a Cantor set and its mapping class group appear in many dynamical contexts\, including \;group \;actions on surfac es\, the study of groups of homeomorphisms on a Cantor set\, and complex d ynamics. \;In this talk\, I will motivate the study of this 'big mappi ng class groups'. I will then present the 'ray \;graph'\, which is a G romov-hyperbolic \;graph \;on which this \;group \;acts by isometries. \; \;
DTEND;TZID=Europe/Zurich:20181106T120000 END:VEVENT BEGIN:VEVENT UID:news347@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181016T103000 SUMMARY:Seminar Algebra and Geometry: Pierre-Marie Poloni and Richard Griff on (University of Basel) DESCRIPTION:TBA X-ALT-DESC:TBA DTEND;TZID=Europe/Zurich:20181016T120000 END:VEVENT BEGIN:VEVENT UID:news324@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20181002T103000 SUMMARY:Seminar Algebra and Geometry: Immanuel van Santen\, Anne Lonjou and Jeremy Blanc (University of Basel) DESCRIPTION:Immanuel van Santen will speak about „Embeddings and tame aut omorphisms in affine geometry"\, \\r\\nAnne Lonjou will explain some link between "Cremona group and geometric group theory"\, and \\r\\nJérémy Blanc will present us "Birational geometry of surfaces and threefolds". X-ALT-DESC:\nImmanuel van Santen will speak about „Embeddings and tame au tomorphisms in affine geometry"\;\, \;\nAnne Lonjou will explain s ome link between "\;Cremona group and geometric group theory"\;\, and \;\nJérémy Blanc will present us "\;Birational geometry of s urfaces and threefolds"\;. DTEND;TZID=Europe/Zurich:20181002T120000 END:VEVENT BEGIN:VEVENT UID:news322@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181204T082628 DTSTART;TZID=Europe/Zurich:20180925T103000 SUMMARY:Seminar Algebra and Geometry: Julia Schneider\, Egor Yasinsky and P hilipp Mekler (University of Basel) DESCRIPTION:Julia will speak about "A_k-singularities of plane curves of fi xed bidegree".\\r\\nEgor will answer to "What transformation groups in alg ebraic\, differential and metric geometry have in common?". \\r\\nPhilipp will speak about "Algebraic Statistics: Gaussian Mixtures and Beyond". X-ALT-DESC:\nJulia will speak about "\;A_k-singularities of plane curve s of fixed bidegree"\;.\nEgor will answer to "\;What transformatio n groups in algebraic\, differential and metric geometry have in common?&q uot\;. \;\nPhilipp will speak about "\;Algebraic Statistics: Gauss ian Mixtures and Beyond"\;. DTEND;TZID=Europe/Zurich:20180925T120000 END:VEVENT BEGIN:VEVENT UID:news644@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T172712 DTSTART;TZID=Europe/Zurich:20180529T103000 SUMMARY:Seminar Algebra and Geometry: Jérémy Blanc (Basel) DESCRIPTION:I will describe a joint work with Stéphane Lamy and Susanna Zi mmermann which provides abelian quotients of the Cremona groups in high dimension. X-ALT-DESC: I will describe a joint work with Stéphane Lamy and Susanna Zi mmermann which provides abelian quotients of the Cremona groups in high dimension. DTEND;TZID=Europe/Zurich:20180529T120000 END:VEVENT BEGIN:VEVENT UID:news643@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T172506 DTSTART;TZID=Europe/Zurich:20180522T103000 SUMMARY:Seminar Algebra and Geometry: Andriy Regeta (Köln) DESCRIPTION:In this talk we are going to discuss the following question: t o which extent a so-called Danielewski surface is determined by its autom orphism group seen as an abstract group or as an ind-group? X-ALT-DESC: In this talk we are going to discuss the following question: t o which extent a so-called Danielewski surface is determined by its autom orphism group seen as an abstract group or as an ind-group? DTEND;TZID=Europe/Zurich:20180522T120000 END:VEVENT BEGIN:VEVENT UID:news642@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T172321 DTSTART;TZID=Europe/Zurich:20180515T103000 SUMMARY:Seminar Algebra and Geometry: Peter Feller (ETHZ) DESCRIPTION:We start by recalling that a smooth algebraic curve of degree d in CP2 is a genus (d-1)(d-2)/2 surface (read `smooth 2-manifold'). The ` Thom Conjecture'\, proven by Kronheimer and Mrowka\, asserts that such al gebraic curves have a surprising minimizing property. We derive consequenc es of the Thom Conjecture for transversal intersections of algebraic curv es with round spheres\, describe the knots one finds as such intersection s following Rudolph\, and give precise instances of the sentiment that th ese intersections constitute very special elements in the so-called smoot h concordance group. In contrast\, in the topological category\, we prove that all knots are topological concordant to such an intersection. Based on joint work with Maciej Borodzik. No knowledge about knot theory and co ncordance theory---the study of 1-manifolds in the 3-dimensional sphere a nd surfaces in 4-dimensional ball bounding them---will be assumed. X-ALT-DESC: We start by recalling that a smooth algebraic curve of degree d in CP2 is a genus (d-1)(d-2)/2 surface (read `smooth 2-manifo ld'). The `Thom Conjecture'\, proven by Kronheimer and Mrowka\, asserts th at such algebraic curves have a surprising minimizing property. We derive consequences of the Thom Conjecture for transversal intersections of alg ebraic curves with round spheres\, describe the knots one finds as such i ntersections following Rudolph\, and give precise instances of the sentim ent that these intersections constitute very special elements in the so-c alled smooth concordance group. In contrast\, in the topological category \, we prove that all knots are topological concordant to such an intersec tion. Based on joint work with Maciej Borodzik. No knowledge about knot th eory and concordance theory---the study of 1-manifolds in the 3-dimension al sphere and surfaces in 4-dimensional ball bounding them---will be assu med. DTEND;TZID=Europe/Zurich:20180515T120000 END:VEVENT BEGIN:VEVENT UID:news641@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T172012 DTSTART;TZID=Europe/Zurich:20180508T103000 SUMMARY:Seminar Algebra and Geometry: Arthur Bik (Bern) DESCRIPTION:Finite-dimensional vector spaces are Noetherian\, i.e. every de scending chain of Zariski-closed subsets stabilizes. For infinite-dimensi onal spaces this is not true. However what can be true is that for some g roup G acting on the space every descending chain of G-stable closed subs ets stablizes. We call spaces for which this holds G-Noetherian. In this talk\, we will go over some known examples and non-examples of spaces th at are Noetherian up to a group action and introduce some new ones. X-ALT-DESC: Finite-dimensional vector spaces are Noetherian\, i.e. every de scending chain of Zariski-closed subsets stabilizes. For infinite-dimensi onal spaces this is not true. However what can be true is that for some g roup G acting on the space every descending chain of G-stable closed subs ets stablizes. We call spaces for which this holds G-Noetherian. In this talk\, we will go over some known examples and non-examples of spaces th at are Noetherian up to a group action and introduce some new ones. DTEND;TZID=Europe/Zurich:20180508T120000 END:VEVENT BEGIN:VEVENT UID:news640@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T171800 DTSTART;TZID=Europe/Zurich:20180424T103000 SUMMARY:Seminar Algebra and Geometry: Mattias Hemmig (Basel) DESCRIPTION:In 2012 Costa constructed a family of unicuspidal curves of deg ree 9 in the projective plane that are pairwise non-equivalent but have isomorphic complements. We show that a family as the one of Costa cannot contain a unicuspidal curve C that admits a line intersecting C only in th e singular point. To state the result more precisely\, if D is any plane c urve and there exists an isomorphism between the complements of C and D\, then the two curves are projectively equivalent\, even though the isomor phism is not necessarily linear. The proof works over an algebraically cl osed field of any characteristic and generalizes a result of Yoshihara (1 984) who proved the claim over the complex numbers. We then use this resu lt to show that any two irreducible curves of degree at most 8 have isomo rphic complements if and only if they are projectively equivalent. X-ALT-DESC: In 2012 Costa constructed a family of unicuspidal curves of deg ree 9 in the projective plane that are pairwise non-equivalent but have isomorphic complements. We show that a family as the one of Costa cannot contain a unicuspidal curve C that admits a line intersecting C< /i> only in the singular point. To state the result more precisely\, if D is any plane curve and there exists an isomorphism between the comp lements of C and D\, then the two curves are projectively e quivalent\, even though the isomorphism is not necessarily linear. The pr oof works over an algebraically closed field of any characteristic and ge neralizes a result of Yoshihara (1984) who proved the claim over the comp lex numbers. We then use this result to show that any two irreducible cur ves of degree at most 8 have isomorphic complements if and only if they a re projectively equivalent. DTEND;TZID=Europe/Zurich:20180424T120000 END:VEVENT BEGIN:VEVENT UID:news634@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190121T162647 DTSTART;TZID=Europe/Zurich:20180417T103000 SUMMARY:Seminar Algebra and Geometry: Andrea Fanelli (Düsseldorf) DESCRIPTION:Even if the precise notion of rationally simply connected varie ty is still not clear in general\, the recent works by de Jong\, He and S tarr produced great interest and new research directions. In the current joint project with Laurent Gruson and Nicolas Perrin\, we study some examp les of Fano varieties in low dimension via explicit birational methods. X-ALT-DESC: Even if the precise notion of rationally simply connected varie ty is still not clear in general\, the recent works by de Jong\, He and S tarr produced great interest and new research directions.
In the cu rrent joint project with Laurent Gruson and Nicolas Perrin\, we study some examples of Fano varieties in low dimension via explicit birational metho ds. DTEND;TZID=Europe/Zurich:20180417T120000 END:VEVENT BEGIN:VEVENT UID:news633@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T172302 DTSTART;TZID=Europe/Zurich:20180403T103000 SUMMARY:Seminar Algebra and Geometry: Pierre-Marie Poloni (Bern) DESCRIPTION:An $\\mathbb{A}^2$-fibration is a flat morphism between complex affine varieties whose fibers are isomorphic to the complex affine plane . In this talk\, we study explicit families $f:\\mathbb{A}^4\\to\\mathbb{ A}^2$ of $\\mathbb{A}^2$-fibrations over the affine plane. The famous Dol gachev-Weisfeiler conjecture predicts that such fibrations are in fact is omorphic to the trivial bundle. We will show that this holds true in some particular examples. For instance\, we will recover a result of Drew Lew is which states that the $\\mathbb{A}^2$-fibration induced by the second Vénéreau polynomial is trivial. Our proof is inspired by a previous work of Kaliman and Zaidenberg and consists in first showing that the conside red fibrations have a fiber bundle structure when restricted over the pun ctured affine plane. This is a joint work in progress with Jérémy Blanc. X-ALT-DESC:An $\\mathbb{A}^2$-fibration is a flat morphism between complex affine varieties whose fibers are isomorphic to the complex affine plane. In this talk\, we study explicit families $f:\\mathbb{A}^4\\to\\mathbb{A }^2$ of $\\mathbb{A}^2$-fibrations over the affine plane.
The famou s Dolgachev-Weisfeiler conjecture predicts that such fibrations are in fa ct isomorphic to the trivial bundle. We will show that this holds true in some particular examples. For instance\, we will recover a result of Dre w Lewis which states that the $\\mathbb{A}^2$-fibration induced by the se cond Vénéreau polynomial is trivial.
Our proof is inspired by a pr evious work of Kaliman and Zaidenberg and consists in first showing that the considered fibrations have a fiber bundle structure when restricted o ver the punctured affine plane.
This is a joint work in progress wit h Jérémy Blanc. DTEND;TZID=Europe/Zurich:20180403T120000 END:VEVENT BEGIN:VEVENT UID:news632@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190121T142447 DTSTART;TZID=Europe/Zurich:20180313T103000 SUMMARY:Seminar Algebra and Geometry: Konstantin Shramov (HSE Moscow) DESCRIPTION:I will speak about finite groups acting by birational automorph isms of surfaces over algebraically non-closed fields\, mostly function f ields. One of important observations here is thata smooth geometrically rational surface S is either birational to a product of a projective line and a conic (in particular\, S is rational provided that it has a point) \, or finite subgroups of its birational automorphism group are bounded. We will also discuss some particular types of surfaces with interesting au tomorphism groups\, including Severi-Brauer surfaces. X-ALT-DESC: I will speak about finite groups acting by birational automorph isms of surfaces over algebraically non-closed fields\, mostly function f ields. One of important observations here is thata smooth geometrically rational surface S is either birational to a product of a projective line and a conic (in particular\, S is rational provided that it has a point) \, or finite subgroups of its birational automorphism group are bounded.< br /> We will also discuss some particular types of surfaces with interest ing automorphism groups\, including Severi-Brauer surfaces. DTEND;TZID=Europe/Zurich:20180313T120000 END:VEVENT BEGIN:VEVENT UID:news631@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190121T141926 DTSTART;TZID=Europe/Zurich:20180306T103000 SUMMARY:Seminar Algebra and Geometry: Hans-Christian Graf v. Bothmer (Hambu rg) DESCRIPTION:I will review some of the history and recent developments of th e rationality question for conic bundles over projective spaces. I will t hen explain our contribution to this question in the case of conic bundle s over IP^3 (joint work with Asher Auel\, Christian Boehning and Alena Pi rutka). X-ALT-DESC: I will review some of the history and recent developments of th e rationality question for conic bundles over projective spaces. I will t hen explain our contribution to this question in the case of conic bundle s over IP^3 (joint work with Asher Auel\, Christian Boehning and Alena Pi rutka). DTEND;TZID=Europe/Zurich:20180306T120000 END:VEVENT BEGIN:VEVENT UID:news652@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190126T193831 DTSTART;TZID=Europe/Zurich:20171212T103000 SUMMARY:Seminar Algebra and Geometry: Sara Durighetto (Ferrara) DESCRIPTION:Let C\, D be two birational subvarieties of the projective spac e Pn. I am interested in understanding when there exists a Cremona modif ication f:  Pn --->Pn  such that  f(C) = D. For the sake of this talk I will restrict to a configuration of lines in P2. In this special case I'll suggest a classification of configurations of lines that are c ontractible to a bunch of points. In doing this I will propose an unexpec ted configuration that seems to violate an established conjecture. X-ALT-DESC: Let C\, D be two birational subvarieties of the projective spac e \;Pn. \;I am interested in understanding when there exists a Cremona modification \;f: \; \;Pn \;--->\;Pn \; \;such th at \; \;f(C) = D. \;For the sake of this talk I will re strict to a configuration of lines in \;P2. \;In this special case I'll suggest a classification of configu rations of lines that are contractible to a bunch of points. In doing thi s I will propose an unexpected configuration that seems to violate an est ablished conjecture. DTEND;TZID=Europe/Zurich:20171212T120000 END:VEVENT BEGIN:VEVENT UID:news651@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190126T192636 DTSTART;TZID=Europe/Zurich:20171121T103000 SUMMARY:Seminar Algebra and Geometry: Susanna Zimmermann (Angers) DESCRIPTION:The Noether-Castelnuovo theorem implies that over algebraically closed fields there is no non-trivial homomorphism from the Cremona grou p of the plane to a finite group. Over non-closed fields there are many\, and I would like to explain some examples. X-ALT-DESC: The Noether-Castelnuovo theorem implies that over algebraically closed fields there is no non-trivial homomorphism from the Cremona grou p of the plane to a finite group. Over non-closed fields there are many\, and I would like to explain some examples. DTEND;TZID=Europe/Zurich:20171121T120000 END:VEVENT BEGIN:VEVENT UID:news650@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190126T192314 DTSTART;TZID=Europe/Zurich:20171107T103000 SUMMARY:Seminar Algebra and Geometry: Andrea Fanelli (Düsseldorf) DESCRIPTION:Fibre-like Fano manifolds naturally appear in the context of th e minimal model program. In this talk I will discuss some examples\, with special focus on: toric varieties\, manifolds with high index and manifo lds with high Picard rank. These have been obtained in recent joint works with Casagrande-Codogni and Codogni-Svaldi-Tasin. X-ALT-DESC: Fibre-like Fano manifolds naturally appear in the context of th e minimal model program. In this talk I will discuss some examples\, with special focus on: toric varieties\, manifolds with high index and manifo lds with high Picard rank. These have been obtained in recent joint works with Casagrande-Codogni and Codogni-Svaldi-Tasin. DTEND;TZID=Europe/Zurich:20171107T120000 END:VEVENT BEGIN:VEVENT UID:news649@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T181307 DTSTART;TZID=Europe/Zurich:20171024T103000 SUMMARY:Seminar Algebra and Geometry: Immanuel van Santen (Basel) DESCRIPTION:This is joint work with Hanspeter Kraft (University of Basel) a nd Andriy Regeta (University of Cologne). The main problem we address in this talk is the characterization of the affine space An by its automorph ism group Aut(An). More precisely\, we ask\, whether the existence of an abstract group isomorphism Aut(X) \\simeq Aut(An) implies the existence of an isomorphism of algebraic varieties X \\simeq An. The following is o ur main result. Main Theorem. Let X be a quasi-affine irreducible variety such that Aut(X) \\simeq Aut(An). Then X \\simeq An if one of the followi ng conditions holds. (1) X is a Q-acyclic open subset of a smooth affine r ational variety\, and dim(X) is a most equal to n\; (2) X is toric and dim (X) is at least equal to n. After giving a brief history on some related r esults that concern the characterisation of geometric objects via their a utomorphisms\, we give the key ideas of the proof of our main result. X-ALT-DESC: This is joint work with Hanspeter Kraft (University of Basel) a nd Andriy Regeta (University of Cologne). The main problem we address in this talk is the characterization of the affine space An by its automorph ism group Aut(An). More precisely\, we ask\, whether the exist ence of an abstract group isomorphism Aut(X) \\simeq Aut(An) i mplies the existence of an isomorphism of algebraic varieties X \\simeq A n. The following is our main result. Main Theorem.
Let X be a quasi-affine irreducible variety such that Aut(X) \\simeq Aut(An). Then X \\simeq An if one of the following conditions holds.
(1) X is a Q-acyclic open subset of a smooth affine rational variety\, and dim(X) is a most equal to n\;
(2) X is toric and dim( X) is at least equal to n. After giving a brief history on some related re sults that concern the characterisation of geometric objects via their au tomorphisms\, we give the key ideas of the proof of our main result. DTEND;TZID=Europe/Zurich:20171024T120000 END:VEVENT BEGIN:VEVENT UID:news648@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190126T201746 DTSTART;TZID=Europe/Zurich:20171010T103000 SUMMARY:Seminar Algebra and Geometry: Frederic Han (Paris 7) DESCRIPTION:After a short introduction to birational transformations of a p rojective space\, we will focus on the case of P3. Few is known about bir ational transformations of P3 and the case of degree 3 is already difficu lt. To explain how things differ in larger degree it is natural to look a t transformations of bidegree (4\,4). In this talk we detail families of examples in degree 3 and bidegree (4\,4) to illustrate this opposition. (Joint work with J. Déserti) X-ALT-DESC: After a short introduction to birational transformations of a p rojective space\, we will focus on the case of P3. Few is known about bir ational transformations of P3 and the case of degree 3 is already difficu lt. To explain how things differ in larger degree it is natural to look a t transformations of bidegree (4\,4). In this talk we detail families of examples in degree 3 and bidegree (4\,4) to illustrate this opposition. (Joint work with J. Déserti) DTEND;TZID=Europe/Zurich:20171010T120000 END:VEVENT BEGIN:VEVENT UID:news647@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T175652 DTSTART;TZID=Europe/Zurich:20171003T103000 SUMMARY:Seminar Algebra and Geometry: Yves de Cornulier (Lyon 1) DESCRIPTION:Given a group G\, a G-action on a set D commensurates a subset M if M differs from each of its G-translates by finitely many elements. C ommensurating actions naturally induce actions on CAT(0) cube complexes. For every irreducible variety X\, we define a set of (virtual) hypersurfa ces\, which contains the set of hypersurfaces of X and on which the group Bir(X) of birational self-transformations of X acts\, extending its part ial action on hypersurfaces. This action commensurates the set of hypersu rfaces of X. This construction thus provides information about the struct ure of Bir(X) and its subgroups. (Joint work with Serge Cantat) X-ALT-DESC: Given a group G\, a G-action on a set D commensurates a subset M if M differs from each of its G-translates by finitely many elements. C ommensurating actions naturally induce actions on CAT(0) cube complexes. For every irreducible variety X\, we define a set of (virtual) hypersurfa ces\, which contains the set of hypersurfaces of X and on which the group Bir(X) of birational self-transformations of X acts\, extending its part ial action on hypersurfaces. This action commensurates the set of hypersu rfaces of X. This construction thus provides information about the struct ure of Bir(X) and its subgroups. (Joint work with Serge Cantat) DTEND;TZID=Europe/Zurich:20171003T120000 END:VEVENT BEGIN:VEVENT UID:news646@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T174546 DTSTART;TZID=Europe/Zurich:20170926T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Basel) DESCRIPTION:Let G be a semisimple algebraic group acting on an affine varie ty X. An orbit O⊂X is called minimal if it is G-isomorphic to the orbi t of highest weight vectors in an irreducible representation of G. These orbits have many interesting properties. E.g. the closure of a minimal or bit in any affine G-variety X is of the form $\\bar O = O \\cup \\{x_0\\} $ where x0 ∈ X is a fixed point\, and they are even characterised by t his property. An affine G-variety X is called small if all non-trivial or bits in X are minimal. It turns out that these varieties have many remark able properties. The most interesting one is that the coordinate ring is a  graded G-algebra. This allows a classification. In fact\, there is an equivalence of categories of small G-varieties with so-called fix-pointe d k*-varieties\, a class of well-understood objects which have been studi ed very carefully in different contexts. A striking consequence is the fol lowing result. Theorem. Let n > 4. Then a smooth $\\SL_n$-variety of dimen sion d < 2n-2 is an $\\SL_n$-vector bundle over a smooth variety of dime nsion d-n. There are also interesting applications to actions of the affin e group $\\Aff_n$. This was the starting point of this joint work with wi th Andriy Regeta and Susanna Zimmermann. X-ALT-DESC: Let G be a semisimple algebraic group acting on an affine varie ty X. An orbit O⊂X is called minimal if it is G-isomorphic to t he orbit of highest weight vectors in an irreducible representation of G. These orbits have many interesting properties. E.g. the closure of a min imal orbit in any affine G-variety X is of the form $\\bar O = O \\cup \\ {x_0\\}$ where x0 \;∈ X is a fixed point\, and they are e ven characterised by this property.
An affine G-variety X is called small if all non-trivial orbits in X are minimal. It turns out th at these varieties have many remarkable properties. The most interesting one is that the coordinate ring is a \; graded G-algebra. This allows a classification. In fact\, there is an equivalence of cat egories of small G-varieties with so-called fix-pointed k*-varieties\, a class of well-understood objects which have been studie d very carefully in different contexts.
A striking consequence is th e following result.
Theorem. Let n >\; 4. Then a smooth $\\SL_n$-v ariety of dimension d <\; 2n-2 is an $\\SL_n$-vector bundle over a smoo th variety of dimension d-n. There are also interesting applications to a ctions of the affine group $\\Aff_n$. This was the starting point of this joint work with with Andriy Regeta and Susanna Zimmermann. DTEND;TZID=Europe/Zurich:20170926T120000 END:VEVENT BEGIN:VEVENT UID:news645@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190125T173135 DTSTART;TZID=Europe/Zurich:20170919T103000 SUMMARY:Seminar Algebra and Geometry: Anne Lonjou (Basel) DESCRIPTION:The Cremona group is the group of birational transformations of the projective plane. It acts on a hyperbolic space which is an infinite dimensional version of the hyperboloid model of Hn. This action is the main recent tool to study the Cremona group. After defining it\, we will study its Voronoï tesselation\, and describe some graphs naturally assoc iated with this construction. Finally we will discuss which of these grap hs are Gromov-hyperbolic. X-ALT-DESC: The Cremona group is the group of birational transformations of the projective plane. It acts on a hyperbolic space which is an infinite dimensional version of the hyperboloid model of Hn. This acti on is the main recent tool to study the Cremona group. After defining it\ , we will study its Voronoï tesselation\, and describe some graphs natur ally associated with this construction. Finally we will discuss which of these graphs are Gromov-hyperbolic. DTEND;TZID=Europe/Zurich:20170919T120000 END:VEVENT BEGIN:VEVENT UID:news660@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T221333 DTSTART;TZID=Europe/Zurich:20170609T103000 SUMMARY:Seminar Algebra and Geometry: Andrea Fanelli (Düseldorf) DESCRIPTION:Del Pezzo fibrations are possible outputs of a 3-fold MMP also in positive characterisitic. A natural question is whether geometrically non-normal del Pezzo surfaces can appear as generic fibre of such a fibr ation. This talk is based on a joint work with S. Schröer. X-ALT-DESC: Del Pezzo fibrations are possible outputs of a 3-fold MMP also in positive characterisitic. A natural question is whether geometrically non-normal del Pezzo surfaces can appear as generic fibre of such a fibr ation. This talk is based on a joint work with S. Schröer. DTEND;TZID=Europe/Zurich:20170609T120000 END:VEVENT BEGIN:VEVENT UID:news659@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T221404 DTSTART;TZID=Europe/Zurich:20170602T103000 SUMMARY:Seminar Algebra and Geometry: Youssef Fares (Amiens) DESCRIPTION:Let c be a rational number and consider the polynomial map φc( x)=x2-c. We are interested in cycles of φc in $\\Q$. More precisely\, we focus on Poonen's conjecture\, according to which every cycle of φc in $ \\Q$ is of length at most 3. In our talk\, we discuss this conjecture usi ng arithmetic\, combinatorial and analytic means. In particular\, we obta in an upper bound of the cardinality of the set of periodic points which we improve in the case c≤2. We finish the talk by giving some propertie s regarding rational numbers c for which φc has a cycle of length ≥ 4. X-ALT-DESC: Let c be a rational number and consider the polynomial map φc(x)=x2-c.
We are interested in cycles of φc in $\\Q$. More precisely\, we focus on Poonen's conjecture\, acc ording to which every cycle of φc in $\\Q$ is of length at mos t 3. In our talk\, we discuss this conjecture using arithmetic\, combinat orial and analytic means. In particular\, we obtain an upper bound of the cardinality of the set of periodic points which we improve in the case c ≤2. We finish the talk by giving some properties regarding rational num bers c for which φc has a cycle of length \;≥ 4. DTEND;TZID=Europe/Zurich:20170602T120000 END:VEVENT BEGIN:VEVENT UID:news658@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T224851 DTSTART;TZID=Europe/Zurich:20170505T103000 SUMMARY:Seminar Algebra and Geometry: Ivan Cheltsov (Edinburgh) DESCRIPTION:The automorphism group of Igusa quartic is the symmetric group of degree 6. There are other quartic threefolds that admits a faithful ac tion of this group. One of them is the famous Burkhardt quartic threefold . Together they form a pencil that contains all $\\mathbb{S}_6$-symmetric quartic threefolds.Arnaud Beauville proved that all but four of these q uartic threeffolds are irrational. Later Cheltsov and Shramov proved that the remaining threefolds in this pencil are rational. In this talk\, I w ill give an alternative prove of both these results. To do this\, I will describe Q-factorizations of the double cover of the four-dimensional pro jective space branched over the Igusa quartic\, which is known as Coble f ourfold. Using this\, I will show that $\\mathbb{S}_6$-symmetric quartic t hreefolds are birational to conic bundles over quintic del Pezzo surfaces whose degeneration curves are contained in the pencil studied by Wiman a nd Edge.This is a joint work with Alexander Kuznetsov and Constantin Shra mov (Moscow). X-ALT-DESC: The automorphism group of Igusa quartic is the symmetric group of degree 6. There are other quartic threefolds that admits a faithful ac tion of this group. One of them is the famous Burkhardt quartic threefold . Together they form a pencil that contains all $\\mathbb{S}_6$-symmetric quartic threefolds.
Arnaud Beauville proved that all but four of t hese quartic threeffolds are irrational. Later Cheltsov and Shramov prove d that the remaining threefolds in this pencil are rational. In this talk \, I will give an alternative prove of both these results. To do this\, I will describe Q-factorizations of the double cover of the four-dimension al projective space branched over the Igusa quartic\, which is known as C oble fourfold. Using this\, I will show that $\\mathbb{S}_6$-symmetric qua rtic threefolds are birational to conic bundles over quintic del Pezzo su rfaces whose degeneration curves are contained in the pencil studied by W iman and Edge.
This is a joint work with Alexander Kuznetsov and Con stantin Shramov (Moscow). DTEND;TZID=Europe/Zurich:20170505T120000 END:VEVENT BEGIN:VEVENT UID:news657@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T221448 DTSTART;TZID=Europe/Zurich:20170428T103000 SUMMARY:Seminar Algebra and Geometry: Marcello Bernardara (Toulouse) DESCRIPTION:Let X be a smooth projective variety over a field k\, and assum e that weak factorization holds (e.g.\, k has characteristic zero).I will introduce the Grothendieck ring of triangulated categories\, and show ho w\, using Bondal-Larsen-Lunts motivic measure\, a subgroup of such ring w ill define a subgroup of the group Bir(X) of birational self-maps of X. A main example is given by the filtration via the motivic dimension\, whic h induces a filtration on Bir(X). As a consequence\, in the case X=Pn\, w e can show that the group generated by the standard Cremona transformatio n and PGL(n+1) is strictly contained in the group contracting rational va rieties\, as soon as n > 4. Another example allows to reconstruct Frumkin 's genus filtration of Bir(X) in the cases where X is a uniruled threefol d. X-ALT-DESC: Let X be a smooth projective variety over a field k\, and assum e that weak factorization holds (e.g.\, k has characteristic zero).
I will introduce the Grothendieck ring of triangulated categories\, and s how how\, using Bondal-Larsen-Lunts motivic measure\, a subgroup of such ring will define a subgroup of the group Bir(X) of birational self-maps o f X. A main example is given by the filtration via the motivic dimension\ , which induces a filtration on Bir(X). As a consequence\, in the case X= Pn\, we can show that the group generated by the standard Crem ona transformation and PGL(n+1) is strictly contained in the group contra cting rational varieties\, as soon as n >\; 4. Another example allows t o reconstruct Frumkin's genus filtration of Bir(X) in the cases where X i s a uniruled threefold. DTEND;TZID=Europe/Zurich:20170428T120000 END:VEVENT BEGIN:VEVENT UID:news656@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T221502 DTSTART;TZID=Europe/Zurich:20170421T103000 SUMMARY:Seminar Algebra and Geometry: Nestor Fernandez Vargas (Montpellier/ Rennes) DESCRIPTION:We are interested in rank 2 parabolic vector bundles over a 2-p unctured elliptic curve C. We will describe the moduli space associated t o these objects\, and state a Torelli theorem.The former moduli space is itself related to the moduli space of rank 2 parabolic bundles over a 5-pu nctured P1. We will explain this link\, recovering at the same time the be autiful geometry of del Pezzo surfaces of degree 4. X-ALT-DESC: We are interested in rank 2 parabolic vector bundles over a 2-p unctured elliptic curve C. We will describe the moduli space associated t o these objects\, and state a Torelli theorem.
The former moduli spa ce is itself related to the moduli space of rank 2 parabolic bundles over a 5-punctured P1. We will explain this link\, recovering at the same time the beautiful geometry of del Pezzo surfaces of degree 4. DTEND;TZID=Europe/Zurich:20170421T120000 END:VEVENT BEGIN:VEVENT UID:news655@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T221514 DTSTART;TZID=Europe/Zurich:20170331T103000 SUMMARY:Seminar Algebra and Geometry: Giosuè Muratore (Roma-Strasbourg) DESCRIPTION:The 2-Fano varieties\, defined by De Jong and Starr\, satisfy s ome higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) k-Fano variety and conjecture the polyhedrality o f the cone of pseudoeffective k-cycles for those varieties in analogy wit h the case k=1. Then\, we calculate some Betti numbers of a large class o f k-Fano varieties to prove some special case of the conjecture. In part icular\, the conjecture is true for all 2-Fano varieties of index ≥n-2\ , and also we complete the classification of weak 2-Fano varieties of Ara ujo and Castravet. X-ALT-DESC: The 2-Fano varieties\, defined by De Jong and Starr\, satisfy s ome higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) k-Fano variety and conjecture the polyhedrality o f the cone of pseudoeffective k-cycles for those varieties in analogy wit h the case k=1. Then\, we calculate some Betti numbers of a large class o f k-Fano varieties to prove some special case of the conjecture. In part icular\, the conjecture is true for all 2-Fano varieties of index ≥n-2\ , and also we complete the classification of weak 2-Fano varieties of Ara ujo and Castravet. DTEND;TZID=Europe/Zurich:20170331T120000 END:VEVENT BEGIN:VEVENT UID:news654@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T224919 DTSTART;TZID=Europe/Zurich:20170317T103000 SUMMARY:Seminar Algebra and Geometry: Yohan Brunebarbe (Zurich) DESCRIPTION:For any positive integers g and n\, let A_g(n) be the moduli sp ace of principally polarized abelian varieties with a level-n structure ( it is a smooth quasi-projective variety for n>2). Building on works of Na del and Noguchi\, Hwang and To have shown that the minimal genus of a cur ve contained in A_g(n) grows with n. We will explain a generalization of this result dealing with subvarieties of any dimension. In particular\, we show that all subvarieties of A_g(n) are of general type when n > 6g. Similar results are true more generally for quotients of bounded symmetri c domains by lattices. X-ALT-DESC:For any positive integers g and n\, let A_g(n) be the moduli spa ce of principally polarized abelian varieties with a level-n structure (i t is a smooth quasi-projective variety for n>\;2). Building on works of Nadel and Noguchi\, Hwang and To have shown that the minimal genus of a curve contained in A_g(n) grows with n. We will explain a generalization of this result dealing with subvarieties of any dimension. In particular\ , we show that all subvarieties of A_g(n) are of general type when n >\ ; 6g. Similar results are true more generally for quotients of bounded s ymmetric domains by lattices. DTEND;TZID=Europe/Zurich:20170317T120000 END:VEVENT BEGIN:VEVENT UID:news653@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T224932 DTSTART;TZID=Europe/Zurich:20170303T103000 SUMMARY:Seminar Algebra and Geometry: Jan Draisma (Bern) DESCRIPTION:Every real or complex matrix admits a singular value decomposit ion\, in which the terms are pairwise orthogonal in a strong sense. Highe r-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention from theoretical computer science and scientific computing. Complementing this existing literature\, I will present an algebro-geometric analysis of the set of orthogonally decomp osable tensors. This analysis features a surprising connection between or thogonally decomposable tensors and semisimple algebras---associative in the case of ordinary or symmetric tensors\, and of compact Lie type in th e case of alternating tensors. (Joint work with Ada Boralevi\, Emil Horobe t\, and Elina Robeva.) X-ALT-DESC: Every real or complex matrix admits a singular value decomposit ion\, in which the terms are pairwise orthogonal in a strong sense. Highe r-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention from theoretical computer science and scientific computing. Complementing this existing literature\, I will present an algebro-geometric analysis of the set of orthogonally decomp osable tensors. This analysis features a surprising connection between or thogonally decomposable tensors and semisimple algebras---associative in the case of ordinary or symmetric tensors\, and of compact Lie type in th e case of alternating tensors.
(Joint work with Ada Boralevi\, Emil Horobet\, and Elina Robeva.) DTEND;TZID=Europe/Zurich:20170303T120000 END:VEVENT BEGIN:VEVENT UID:news670@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225047 DTSTART;TZID=Europe/Zurich:20161216T140000 SUMMARY:Seminar Algebra and Geometry: Eleonora Di Nezza (Imperial College L ondon) DESCRIPTION:The geometry and topology of the space of Kähler metrics on a compact Kähler manifold is a classical subject\, first systematically st udied by Calabi in relation with the existence of extremal Kähler metric s. Then\, Mabuchi proposed a Riemannian structure on the space of Kähler metrics under which it (formally) becomes a non-positive curved infinite dimensional space. Chen later proved that this is a metric space of non -positive curvature in the sense of Alexandrov and its metric completion was characterized only recently by Darvas. In this talk we will talk abou t the extension of such a theory to the setting where the compact Kähler manifold is replaced by a compact singular normal Kähler space. As one application we give an analytical criterion for the existence of Kähler- Einstein metrics on certain mildly singular Fano varieties\, an analogous to a criterion in the smooth case due to Darvas and Rubinstein.This is b ased on a joint work with Vincent Guedj. X-ALT-DESC: The geometry and topology of the space of Kähler metrics on a compact Kähler manifold is a classical subject\, first systematically st udied by Calabi in relation with the existence of extremal Kähler metric s. Then\, Mabuchi proposed a Riemannian structure on the space of Kähler metrics under which it (formally) becomes a non-positive curved infinite dimensional space. Chen later proved that this is a metric space of non -positive curvature in the sense of Alexandrov and its metric completion was characterized only recently by Darvas. In this talk we will talk abou t the extension of such a theory to the setting where the compact Kähler manifold is replaced by a compact singular normal Kähler space. As one application we give an analytical criterion for the existence of Kähler- Einstein metrics on certain mildly singular Fano varieties\, an analogous to a criterion in the smooth case due to Darvas and Rubinstein.
Thi s is based on a joint work with Vincent Guedj. DTEND;TZID=Europe/Zurich:20161216T153000 END:VEVENT BEGIN:VEVENT UID:news669@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225059 DTSTART;TZID=Europe/Zurich:20161216T103000 SUMMARY:Seminar Algebra and Geometry: Zsolt Patakfalvi (EPFL) DESCRIPTION:Stable varieties are higher dimensional generalizations of stab le curves. Their moduli space contains an open locus parametrizing varie ties of general type up to birational equivalence\, just as the space of stable curves contains the space of smooth curves in dimension one. Furth ermore\, also similarly to the one dimensional picture\, it provides a co mpactification of the above locus\, which is known in characteristic zero but it is only conjectural in positive characteristic in dimension at le ast two. I will present a work in progress aiming to prove the projectivi ty of every proper subspace of the moduli space of stable surfaces in cha racteristic greater than 5. X-ALT-DESC: Stable varieties are higher dimensional generalizations of stab le curves. Their moduli space contains an open locus parametrizing varie ties of general type up to birational equivalence\, just as the space of stable curves contains the space of smooth curves in dimension one. Furth ermore\, also similarly to the one dimensional picture\, it provides a co mpactification of the above locus\, which is known in characteristic zero but it is only conjectural in positive characteristic in dimension at le ast two. I will present a work in progress aiming to prove the projectivi ty of every proper subspace of the moduli space of stable surfaces in cha racteristic greater than 5. DTEND;TZID=Europe/Zurich:20161216T120000 END:VEVENT BEGIN:VEVENT UID:news668@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225134 DTSTART;TZID=Europe/Zurich:20161209T103000 SUMMARY:Seminar Algebra and Geometry: Peter Feller (Bonn) DESCRIPTION:After a brief introduction to plane curve singularities\, we re cast some of their classical invariants in terms of modern knot theory. T hen we will see connections between purely algebraic questions about def ormations of singularities and purely knot theoretic questions about cobo rdisms between knots\, and answer some of them. This talk aims to be elem entary and will not assume familiarity with knot theory or singularity th eory. X-ALT-DESC: After a brief introduction to plane curve singularities\, we re cast some of their classical invariants in terms of modern knot theory. T hen we will see connections between purely algebraic questions about def ormations of singularities and purely knot theoretic questions about cobo rdisms between knots\, and answer some of them. This talk aims to be elem entary and will not assume familiarity with knot theory or singularity th eory. DTEND;TZID=Europe/Zurich:20161209T120000 END:VEVENT BEGIN:VEVENT UID:news667@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225148 DTSTART;TZID=Europe/Zurich:20161111T103000 SUMMARY:Seminar Algebra and Geometry: Ruth Kellerhals (Fribourg) DESCRIPTION:This talk starts with a survey about hyperbolic volume in three dimensions\, dilogarithms and zeta values.The main part deals with simil ar features and questions about hyperbolic volume of (non-)arithmetic Cox eter orbifolds of higher dimensions. We discuss the volume problem for ce rtain Coxeter pyramids. This family gives rise to interesting (non-)arith metic reflection groups whose commensurability classification has recentl y been performed (joint work with R. Guglielmetti and M. Jacquemet).This is a report about ongoing work. X-ALT-DESC: This talk starts with a survey about hyperbolic volume in three dimensions\, dilogarithms and zeta values.
The main part deals with similar features and questions about hyperbolic volume of (non-)arithmet ic Coxeter orbifolds of higher dimensions. We discuss the volume problem for certain Coxeter pyramids. This family gives rise to interesting (non- )arithmetic reflection groups whose commensurability classification has r ecently been performed (joint work with R. Guglielmetti and M. Jacquemet) .
This is a report about ongoing work. DTEND;TZID=Europe/Zurich:20161111T120000 END:VEVENT BEGIN:VEVENT UID:news666@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225159 DTSTART;TZID=Europe/Zurich:20161104T103000 SUMMARY:Seminar Algebra and Geometry: Diletta Martinelli (University of Edi nburgh) DESCRIPTION:Finding minimal models is the first step in the birational cla ssification of smooth projective varieties. After it is established that a minimal model exists\, some natural question arise\, such as: is the mi nimal model unique? If not\, how many are they? After recalling all the n ecessary notions of the Minimal Model Program\, I will explain that varie ties of general type admit a finite number of minimal models. I will talk about a recent joint project with Stefan Schreieder and Luca Tasin\, whe re we prove that in the case of threefold this number is bounded by a con stant depending only on the Betti numbers. I will also show that in some cases it is possible to compute this constant explicitly. X-ALT-DESC: Finding minimal models is the first step in the birational cla ssification of smooth projective varieties. After it is established that a minimal model exists\, some natural question arise\, such as: is the mi nimal model unique? If not\, how many are they? After recalling all the n ecessary notions of the Minimal Model Program\, I will explain that varie ties of general type admit a finite number of minimal models. I will talk about a recent joint project with Stefan Schreieder and Luca Tasin\, whe re we prove that in the case of threefold this number is bounded by a con stant depending only on the Betti numbers. I will also show that in some cases it is possible to compute this constant explicitly. DTEND;TZID=Europe/Zurich:20161104T120000 END:VEVENT BEGIN:VEVENT UID:news665@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225215 DTSTART;TZID=Europe/Zurich:20161021T103000 SUMMARY:Seminar Algebra and Geometry: Jesus Martinez (MPIM Bonn) DESCRIPTION:We study variations of GIT quotients of log pairs (X\,D) where X is a hypersurface of some fixed degree and D is a hyperplane section. G IT is known to provide a finite number of possible compactifications of s uch pairs\, depending on one parameter. Any two such compactifications ar e related by birational transformations. We describe an algorithm to stud y the stability of the Hilbert scheme of these pairs\, and apply our alg orithm to the case of cubic surfaces. Finally\, we relate these compactif ications to the (conjectural) moduli space of logK-semistable pairs showi ng that any log K-stable pair is an element of our moduli and that there is a canonically defined CM line bundle that polarizes our moduli. This i s a joint work with Patricio Gallardo (University of Georgia) and Cristia no Spotti (Aarhus University). X-ALT-DESC: We study variations of GIT quotients of log pairs (X\,D) where X is a hypersurface of some fixed degree and D is a hyperplane section. G IT is known to provide a finite number of possible compactifications of s uch pairs\, depending on one parameter. Any two such compactifications ar e related by birational transformations. We describe an algorithm to stud y the stability of the Hilbert scheme of these pairs\, and apply our alg orithm to the case of cubic surfaces. Finally\, we relate these compactif ications to the (conjectural) moduli space of logK-semistable pairs showi ng that any log K-stable pair is an element of our moduli and that there is a canonically defined CM line bundle that polarizes our moduli. This i s a joint work with Patricio Gallardo (University of Georgia) and Cristia no Spotti (Aarhus University). DTEND;TZID=Europe/Zurich:20161021T120000 END:VEVENT BEGIN:VEVENT UID:news664@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225229 DTSTART;TZID=Europe/Zurich:20161014T103000 SUMMARY:Seminar Algebra and Geometry: Stefano Urbinati (Padova) DESCRIPTION:Given a Mori Dream Space X we construct via tropicalization a m odel dominating all the small Q-factorial modifications. Via this constr uction we recover a Minkowski bases for the Newton-Okunkov bodies on X an d hence the movable cone for X.This is a work in progress with Elisa Posti nghel. X-ALT-DESC: Given a Mori Dream Space X we construct via tropicalization a m odel dominating all the small Q-factorial modifications. Via this constr uction we recover a Minkowski bases for the Newton-Okunkov bodies on X an d hence the movable cone for X.
This is a work in progress with Elisa Postinghel. DTEND;TZID=Europe/Zurich:20161014T120000 END:VEVENT BEGIN:VEVENT UID:news663@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225243 DTSTART;TZID=Europe/Zurich:20161007T103000 SUMMARY:Seminar Algebra and Geometry: Hannah Bergner (Freiburg) DESCRIPTION:Let J be a (complex) semi-simple Jordan algebra\, and consider the diagonal action of its automorphism group on the n-fold product of J. In this talk\, geometric properties of this action are studied. In parti cular\, a characterization of the closed orbits is given\, which is simil ar to the description in the case where a reductive linear algebraic grou p acts on (the n-fold product of) its Lie algebra. X-ALT-DESC: Let J be a (complex) semi-simple Jordan algebra\, and consider the diagonal action of its automorphism group on the n-fold product of J. In this talk\, geometric properties of this action are studied. In parti cular\, a characterization of the closed orbits is given\, which is simil ar to the description in the case where a reductive linear algebraic grou p acts on (the n-fold product of) its Lie algebra. DTEND;TZID=Europe/Zurich:20161007T120000 END:VEVENT BEGIN:VEVENT UID:news662@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225255 DTSTART;TZID=Europe/Zurich:20160930T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Basel) DESCRIPTION:The aim is to give a modern proof of the famous Theorem of A. W eil showing that for every rational action of an algebraic group G on a variety X there is a regular action of G on a variety Y and a G-equivar iant birational map X → Y. As a guideline we use an approach given by D. Zaitsev (J. Lie Theory 5\, 1995). X-ALT-DESC: The aim is to give a modern proof of the famous Theorem of A. W eil showing that for every rational action of an algebraic group G on a variety X there is a regular action of G on a variety Y and a G-equivar iant birational map X \;→ Y. As a guideline we use an approach giv en by D. Zaitsev (J. Lie Theory 5\, 1995). DTEND;TZID=Europe/Zurich:20160930T120000 END:VEVENT BEGIN:VEVENT UID:news661@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225309 DTSTART;TZID=Europe/Zurich:20160923T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Basel) DESCRIPTION:The aim is to give a modern proof of the famous Theorem of A. W eil showing that for every rational action of an algebraic group G on a variety X there is a regular action of G on a variety Y and a G-equivarian t birational map X → Y. As a guideline we use an approach given by D. Zaitsev (J. Lie Theory 5\, 1995). X-ALT-DESC: The aim is to give a modern proof of the famous Theorem of A. W eil showing that for every rational action of an algebraic group G on a variety X there is a regular action of G on a variety Y and a G-equivarian t birational map X \;→ Y. As a guideline we use an approach given b y D. Zaitsev (J. Lie Theory 5\, 1995). DTEND;TZID=Europe/Zurich:20160923T120000 END:VEVENT BEGIN:VEVENT UID:news683@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225424 DTSTART;TZID=Europe/Zurich:20160602T103000 SUMMARY:Seminar Algebra and Geometry: Anne Lonjou (Toulouse) DESCRIPTION:In this talk\, we will study a 2-dimensional simplicial complex on which the Cremona group acts. After defining this complex introduced by Wright in 1992\, we will see some of its properties. Then\, we will di scuss about some work in progress aimed at showing that this complex is G romov hyperbolic. X-ALT-DESC:In this talk\, we will study a 2-dimensional simplicial complex on which \;the Cremona group acts. After defining this complex introdu ced by Wright \;in 1992\, we will see some of its properties. Then\, w e will discuss about \;some work in progress aimed at showing that thi s complex is Gromov hyperbolic. DTEND;TZID=Europe/Zurich:20160602T120000 END:VEVENT BEGIN:VEVENT UID:news682@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225437 DTSTART;TZID=Europe/Zurich:20160527T103000 SUMMARY:Seminar Algebra and Geometry: Tatiana Bandman (Bar Ilan) DESCRIPTION:A group G  is called Jordan  if there is a positive integer J   = JG  such that every nite subgroup B  of G  contains a commutative subgroup A c B  such that A  is normal in B  and the index [B  : A ] <= J . There is no example of an algebraic variety with the non-Jordan au tomorphism group. It is known that the group of birational automorphisms B ir(X ) of a projective variety X  is Jordan if it is not uniruled and is not Jordan if X  is birational to the direct product of a projective spac e with an abelian variety. I will give an introduction to the topic and di scuss the case when variety X  is a conic bundle over a non-uniruled vari ety Y  and is not birational to Y x P^1:  This is a joint work with Y. Zarhin. X-ALT-DESC: A group G \; is called Jordan \; if there is a positive integer J \; = JG \; \;such that every nite subgroup B \; of G \; contains a commutative subgroup A c \;B \; such that A \; is normal in B \; and the index [B \; : A ]<\;= \;J . There is no example of an algebraic variety with the non-Jordan automor phism group. It is known that the group of birational automorphisms Bir(X ) of a projective variety X \; is Jordan if it is not uniruled and is not Jordan if X \; is birational to the direct product of a projective space with an abelian variety. I will give an introduction to the topic a nd discuss the case when variety X \; is a conic bundle over a non-uni ruled variety Y \; and is not birational to Y x \;P^1:  \; This is a joint work with Y. Zarhin. DTEND;TZID=Europe/Zurich:20160527T120000 END:VEVENT BEGIN:VEVENT UID:news681@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225453 DTSTART;TZID=Europe/Zurich:20160513T103000 SUMMARY:Seminar Algebra and Geometry: Vladimir Lazic (Bonn) DESCRIPTION:Given an algebraic variety\, finding non-trivial morphisms to other varieties is one of the fundamental problems in algebraic geometry. Mori and others solved this problem in the 1980s for varieties whose can onical class is not non-negative on all curves. The question remains open for other varieties. However\, in this talk I will report on a recent p rogress on this problem in a joint work with Thomas Peternell. I will con centrate on varieties with trivial canonical class and on Calabi-Yau mani folds in particular. X-ALT-DESC: Given an algebraic variety\, finding non-trivial morphisms to other varieties is one of the fundamental problems in algebraic geometry. Mori and others solved this problem in the 1980s for varieties whose can onical class is not non-negative on all curves. The question remains open for other varieties. However\, in this talk I will report on a recent p rogress on this problem in a joint work with Thomas Peternell. I will con centrate on varieties with trivial canonical class and on Calabi-Yau mani folds in particular. DTEND;TZID=Europe/Zurich:20160513T120000 END:VEVENT BEGIN:VEVENT UID:news680@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225509 DTSTART;TZID=Europe/Zurich:20160429T103000 SUMMARY:Seminar Algebra and Geometry: Arnaud Girand (Rennes) DESCRIPTION:In this talk we will discuss how various methods from biration al and algebraic geometry may be used to classify and explicitly construc t a specific family of isomonodromic deformations over the five punctured sphere. These objects (which we will introduce during the course of the talk) have been linked to the study of algebraic solutions of certain pa rtial differential equations and offer some interesting ways of bridging some algebraic\, geometric and analytical topics. X-ALT-DESC: In this talk we will discuss how various methods from biration al and algebraic geometry may be used to classify and explicitly construc t a specific family of isomonodromic deformations over the five punctured sphere. These objects (which we will introduce during the course of the talk) have been linked to the study of algebraic solutions of certain pa rtial differential equations and offer some interesting ways of bridging some algebraic\, geometric and analytical topics. DTEND;TZID=Europe/Zurich:20160429T120000 END:VEVENT BEGIN:VEVENT UID:news679@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225522 DTSTART;TZID=Europe/Zurich:20160408T103000 SUMMARY:Seminar Algebra and Geometry: Luca Tasin (Bonn) DESCRIPTION:Generalising a question of Hirzebruch\, Kotschick asked the fol lowing: which Chern numbers are determined up to finite ambiguity by the underlying smooth manifold? Together with S. Schreieder\, I treated this question in dimension higher than 3. After explaining such results\, I w ill talk about the 3 dimensional case\, where it is believed that Chern n umbers are bounded. Results in this direction have been obtained in a rec ent preprint with P. Cascini\, where tools from the Minimal Model Program have been used\, combined with topology's and arithmetic's techniques. X-ALT-DESC: Generalising a question of Hirzebruch\, Kotschick asked the fol lowing: which Chern numbers are determined up to finite ambiguity by the underlying smooth manifold? Together with S. Schreieder\, I treated this question in dimension higher than 3. After explaining such results\, I w ill talk about the 3 dimensional case\, where it is believed that Chern n umbers are bounded. Results in this direction have been obtained in a rec ent preprint with P. Cascini\, where tools from the Minimal Model Program have been used\, combined with topology's and arithmetic's techniques. DTEND;TZID=Europe/Zurich:20160408T120000 END:VEVENT BEGIN:VEVENT UID:news678@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225533 DTSTART;TZID=Europe/Zurich:20160401T103000 SUMMARY:Seminar Algebra and Geometry: Daniel Panazzolo (Mulhouse) DESCRIPTION:PSL(2\,C)\, the exponential and some new free groups X-ALT-DESC:PSL(2\,C)\, the exponential and some new free groups DTEND;TZID=Europe/Zurich:20160401T120000 END:VEVENT BEGIN:VEVENT UID:news677@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225547 DTSTART;TZID=Europe/Zurich:20160318T103000 SUMMARY:Seminar Algebra and Geometry: Giulio Codogni (Roma Tre) DESCRIPTION:We prove (using algebro-geometric methods) two results that all ow to test the positivity of the Donaldson-Futaki weights of arbitrary p olarised varieties via test-configurations which are equivariant with res pect to a maximal torus in the automorphism group. It follows in particul ar that there is a purely algebro-geometric proof of the K-stability of p rojective spaces (or more generally of smooth toric Fanos with vanishing Futaki character\, as well as of the examples of non-toric Kahler-Einstei n Fano threefolds due to Ilten and Suss) and that K-stability for toric p olarised manifolds can be tested via toric test-configurations. A further application is a proof of the K-stability of constant scalar curvature p olarised manifolds with continuous automorphisms. Our approach is based o n the method of filtrations introduced by Wytt Nystrom and Szekelyhidi. T his is a joint work with J. Stoppa. X-ALT-DESC: We prove (using algebro-geometric methods) two results that all ow to test the positivity of the Donaldson-Futaki weights of arbitrary p olarised varieties via test-configurations which are equivariant with res pect to a maximal torus in the automorphism group. It follows in particul ar that there is a purely algebro-geometric proof of the K-stability of p rojective spaces (or more generally of smooth toric Fanos with vanishing Futaki character\, as well as of the examples of non-toric Kahler-Einstei n Fano threefolds due to Ilten and Suss) and that K-stability for toric p olarised manifolds can be tested via toric test-configurations. A further application is a proof of the K-stability of constant scalar curvature p olarised manifolds with continuous automorphisms. Our approach is based o n the method of filtrations introduced by Wytt Nystrom and Szekelyhidi. T his is a joint work with J. Stoppa. DTEND;TZID=Europe/Zurich:20160318T120000 END:VEVENT BEGIN:VEVENT UID:news676@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225558 DTSTART;TZID=Europe/Zurich:20160311T103000 SUMMARY:Seminar Algebra and Geometry: Jean Fasel (Grenoble) DESCRIPTION:In this talk\, which is a joint work with Adrien Dubouloz\, we will explain that the unstable homotopy category is unable to distinguish between the affine space of dimension 3 and the Koras-Russell threefolds of the first kind. We will first make some historical remarks and then spend some time to explain the basic features of the unstable homotopy ca tegory\, in particular how to distinguish isomorphisms in some special ca ses. We will then proceed with the proof of the above claim. X-ALT-DESC: In this talk\, which is a joint work with Adrien Dubouloz\, we will explain that the unstable homotopy category is unable to distinguish between the affine space of dimension 3 and the Koras-Russell threefolds of the first kind. We will first make some historical remarks and then spend some time to explain the basic features of the unstable homotopy ca tegory\, in particular how to distinguish isomorphisms in some special ca ses. We will then proceed with the proof of the above claim. DTEND;TZID=Europe/Zurich:20160311T120000 END:VEVENT BEGIN:VEVENT UID:news675@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225615 DTSTART;TZID=Europe/Zurich:20160310T110000 SUMMARY:Seminar Algebra and Geometry: Alexander Perepechko (Moscow) DESCRIPTION:It is well known that A1-fibrations are of particular interest in the study of automorphism groups of affine surfaces. That is\, descrip tion of automorphism groups is based on subgroups preserving A1-fibration s\, except for surfaces without such fibrations. We provide a method to directly compute these subgroups in terms of a boundary divisor of an SNC -completion. We also use the concepts of arc spaces and formal neighbourh oods. This allows us to establish the following structure of a subgroup p reserving a A1-fibration. Up to a finite index\, it is a semidirect produ ct of an abelian unipotent subgroup acting by translations on fibers and of a finite-dimensional subgroup that fixes a certain section.In particul ar\, we derive an example of a surface with infinite discrete automorphism group. X-ALT-DESC: It is well known that A1-fibrations are of particular interest in the study of automorphism groups of affine surfaces. That is\, descrip tion of automorphism groups is based on subgroups preserving A1-fibration s\, except for surfaces without such fibrations. We provide a method to directly compute these subgroups in terms of a boundary divisor of an SNC -completion. We also use the concepts of arc spaces and formal neighbourh oods. This allows us to establish the following structure of a subgroup p reserving a A1-fibration. Up to a finite index\, it is a semidirect produ ct of an abelian unipotent subgroup acting by translations on fibers and of a finite-dimensional subgroup that fixes a certain section.
In pa rticular\, we derive an example of a surface with infinite discrete automo rphism group. DTEND;TZID=Europe/Zurich:20160310T120000 END:VEVENT BEGIN:VEVENT UID:news674@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225629 DTSTART;TZID=Europe/Zurich:20160308T140000 SUMMARY:Seminar Algebra and Geometry: De-Qi Zhang (Singapore) DESCRIPTION:We will report our recent results on solvable groups G of autom orphisms of normal projective varieties X. One machinery we use is the e quivariant minimal model program. One purpose is to know more geometry of X from the existence of such G acting on X. X-ALT-DESC: We will report our recent results on solvable groups G of autom orphisms of normal projective varieties X. One machinery we use is the e quivariant minimal model program. One purpose is to know more geometry of X from the existence of such G acting on X. DTEND;TZID=Europe/Zurich:20160308T150000 END:VEVENT BEGIN:VEVENT UID:news673@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225652 DTSTART;TZID=Europe/Zurich:20160303T103000 SUMMARY:Seminar Algebra and Geometry: Hamid Ahmadinezhad (Bristol) DESCRIPTION:I will give an overview of the geometry of Fano 3-folds after M ori theory. After discussing past approaches to the classification\, I wi ll highlight why such attempts seem hopeless. Building on recent advances in the geometry of Fanos\, I introduce a new viewpoint on the classific ation problem. A main emphasis will be given to the unpredicted behaviour of the first examples of non-complete intersection Fanos\, discovered in a joint work with Takuzo Okada. X-ALT-DESC: I will give an overview of the geometry of Fano 3-folds after M ori theory. After discussing past approaches to the classification\, I wi ll highlight why such attempts seem hopeless. Building on recent advances in the geometry of Fanos\, I introduce a new viewpoint on the classific ation problem. A main emphasis will be given to the unpredicted behaviour of the first examples of non-complete intersection Fanos\, discovered in a joint work with Takuzo Okada. DTEND;TZID=Europe/Zurich:20160303T120000 END:VEVENT BEGIN:VEVENT UID:news672@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225702 DTSTART;TZID=Europe/Zurich:20160226T103000 SUMMARY:Seminar Algebra and Geometry: Alvaro Liendo (Talca) DESCRIPTION:This is a joint work with A. Dubouloz.In this talk we present s ome recent results about additive group actions on non-necessarily affine algebraic varieties that generalize the usual description of additive g roup actions on affine varieties via locally nilpotent derivations. In pa rticular\, we provide a characterization of additive group actions on a w ide class of algebraic varieties in terms of a certain type of integrable vector fields. X-ALT-DESC: This is a joint work with A. Dubouloz.
In this talk we pre sent some recent results about additive group actions on non-necessarily affine algebraic varieties that generalize the usual description of addit ive group actions on affine varieties via locally nilpotent derivations. In particular\, we provide a characterization of additive group actions o n a wide class of algebraic varieties in terms of a certain type of inte grable vector fields. DTEND;TZID=Europe/Zurich:20160226T120000 END:VEVENT BEGIN:VEVENT UID:news671@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T225715 DTSTART;TZID=Europe/Zurich:20160205T093000 SUMMARY:Seminar Algebra and Geometry: François Dumas (Clermont-Ferrand) DESCRIPTION:The natural algebraic question of extending a group action on a commutative algebra A of "functions" to a noncommutative algebra of dif ferential (or rational differential\, or pseudodifferential) "operators" with coefficients in A is closely related to the study of deformations of A.In the particular case of homography groups\, we will give in this talk an overview of some results about this topic involving transvectants\, mo dular forms and Rankin-Cohen brackets. X-ALT-DESC: The natural algebraic question of extending a group action on a commutative algebra A of "\;functions"\; to a noncommutative alg ebra of differential (or rational differential\, or pseudodifferential) "\;operators"\; with coefficients in A is closely related to the s tudy of deformations of A.
In the particular case of homography grou ps\, we will give in this talk an overview of some results about this topi c involving transvectants\, modular forms and Rankin-Cohen brackets. DTEND;TZID=Europe/Zurich:20160205T110000 END:VEVENT BEGIN:VEVENT UID:news694@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230240 DTSTART;TZID=Europe/Zurich:20151211T103000 SUMMARY:Seminar Algebra and Geometry: Federico Lo Bianco (Rennes) DESCRIPTION:An automorphism f acting on a complex projective (or\, more ge nerally\, compact Kaehler) manifold X induces by pull-back a linear isomo rphism f* of the cohomology of X. The study of the possible isomorphisms that can be realized this way is interesting per se and also has importan t applications in the study of the dynamics of f: for example\, the topol ogical entropy of f\, measuring the chaos created by repeatedly applying f\, can be recovered from the eigenvalues of f*. If X is a surface the si tuation is well understood: if f* is not of finite order\, then either it is virtually unipotent with only one non-trivial Jordan block of dimensi on 3\, or semi-simple with only two eigenvalues with module different tha n 1. I will present the similar results I obtained with Cantat for threef olds and show their optimality with examples on complex tori. X-ALT-DESC: An automorphism f acting on a complex projective (or\, more ge nerally\, compact Kaehler) manifold X induces by pull-back a linear isomo rphism f* of the cohomology of X. The study of the possible iso morphisms that can be realized this way is interesting per se and also ha s important applications in the study of the dynamics of f: for example\, the topological entropy of f\, measuring the chaos created by repeatedl y applying f\, can be recovered from the eigenvalues of f*. If X is a surface the situation is well understood: if f* is not of finite order\, then either it is virtually unipotent with only one no n-trivial Jordan block of dimension 3\, or semi-simple with only two eige nvalues with module different than 1. I will present the similar results I obtained with Cantat for threefolds and show their optimality with exam ples on complex tori. DTEND;TZID=Europe/Zurich:20151211T120000 END:VEVENT BEGIN:VEVENT UID:news693@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230253 DTSTART;TZID=Europe/Zurich:20151204T103000 SUMMARY:Seminar Algebra and Geometry: Jung-Kyu Canci (Basel) DESCRIPTION:In a recent work in collaboration with Salomon Vishkautasan\, w e provide a complete classification of possible graphs of rational prepe riodic points of endomorphisms of the projective line of degree 2 define d over the rationals with a rational periodic critical point of period 2 \, under the assumption that these maps have no periodic points of perio d at least 5. We explain how this extends results of Poonen on quadratic  polynomials. We show that there are 13 possible graphs\, and that such maps have at most 9 rational preperiodic points. X-ALT-DESC: In a recent work in collaboration with Salomon Vishkautasan\, w e provide a complete classification of possible graphs of rational prepe riodic \;points of endomorphisms of the projective line of degree 2 d efined over the rationals with \;a rational periodic critical point of period 2\, under the assumption that these maps have no \;periodic p oints of period at least 5. We explain how this extends results of Poonen on quadratic \;polynomials. We show that there are 13 possible graph s\, and that such maps have at most 9 \;rational preperiodic points. DTEND;TZID=Europe/Zurich:20151204T120000 END:VEVENT BEGIN:VEVENT UID:news692@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230306 DTSTART;TZID=Europe/Zurich:20151113T103000 SUMMARY:Seminar Algebra and Geometry: Emilie Dufresne (Durham) DESCRIPTION:The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Fo r a finite group acting linearly on a vector space\, a separating set is simply a set of invariants whose elements separate the orbits o the acti on. Such a set need not generate the ring of invariants. In this talk\, w e give lower bounds on the size of separating sets based on the geometry of the action. These results are obtained via the study of the local coho mology with support at an arrangement of linear subspaces naturally arisi ng from the action.(Joint with Jack Jeffries) X-ALT-DESC: The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Fo r a finite group acting linearly on a vector space\, a separating set is simply a set of invariants whose elements separate the orbits o the acti on. Such a set need not generate the ring of invariants. In this talk\, w e give lower bounds on the size of separating sets based on the geometry of the action. These results are obtained via the study of the local coho mology with support at an arrangement of linear subspaces naturally arisi ng from the action.
(Joint with Jack Jeffries) DTEND;TZID=Europe/Zurich:20151113T120000 END:VEVENT BEGIN:VEVENT UID:news691@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230316 DTSTART;TZID=Europe/Zurich:20151106T103000 SUMMARY:Seminar Algebra and Geometry: Elisa Gorla (Neuchâtel) DESCRIPTION:In this talk I will discuss a new idea for studying initial id eals and generic initial ideals of ideals in a polynomial ring graded ove r Zm. \\r\\nThese ideas will then be applied to the study of universal Gr oebner bases of ideals of minors\, which admit such a grading. The main t ools and concepts are Zm gradings\, multigraded Hilbert series\, universa l Groebner bases\, initial and generic initial ideals. I will introduce a nd study two families of multigraded ideals with the property that any tw o ideals in the same family that have the same Hilbert series also have the same generic initial ideal. I will show that ideals of minors belong to one of these families\, and derive some result about their universal G roebner bases. X-ALT-DESC: In this talk I will discuss a new idea for studying initial id eals and generic initial ideals of ideals in a polynomial ring graded ove r Zm. \nThese ideas will then be applied to the study of unive rsal Groebner bases of ideals of minors\, which admit such a grading. The main tools and concepts are Zm gradings\, multigraded Hilbert series\, universal Groebner bases\, initial and generic initial ideals. I will introduce and study two families of multigraded ideals with the pr operty that any two ideals in the same family that have the same Hilbert series also have the same generic initial ideal. I will show that ideals of minors belong to one of these families\, and derive some result about their universal Groebner bases. DTEND;TZID=Europe/Zurich:20151106T120000 END:VEVENT BEGIN:VEVENT UID:news690@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230333 DTSTART;TZID=Europe/Zurich:20151030T103000 SUMMARY:Seminar Algebra and Geometry: Enrica Floris (MPI-Bonn) DESCRIPTION:Let X be a smooth algebraic surface. A foliation F on X is\, ro ughly speaking\, a subline bundle TF of the tangent bundle of X. The dual of TF is called the canonical bundle of the foliation KF. In the last fe w years birational methods have been successfully used in order to study f oliations. More precisely\, geometric properties of the foliation are tran slated into properties of the canonical bundle of the foliation. One of t he most important invariants describing the properties of a line bundle L is its Kodaira dimension kod(L)\, which measures the growth of the globa l sections of L and its tensor powers. The Kodaira dimension of a foliatio n F is defined as the Kodaira dimension of its canonical bundle kod(KF). I n their fundamental works\, Brunella and McQuillan give a classfication o f foliations on surfaces on the model of Enriques-Kodaira classification of surfaces. The next step is the study of the behaviour of families of f oliations. Brunella proves that\, for a family of foliations (Xt\, Ft) of dimension one on surfaces\, satisfying certain hypotheses of regularity\ , the Kodaira dimension of the foliation does not depend on t. By analogy with Siu's Invariance of Plurigenera\, it is natural to ask whether for a family of foliations (Xt\, Ft) the dimensions of global sections of the canonical bundle and its powers depend on t. In this talk we will discu ss to which extent an Invariance of Plurigenera for foliations is true an d under which hypotheses on the family of foliations it holds. X-ALT-DESC:Let X be a smooth algebraic surface. A foliation F on X is\, rou ghly speaking\, a subline bundle TF of the tangent bundle of X . The dual of TF is called the canonical bundle of the foliati on KF. In the last few years birational methods have been succe ssfully used in order to study foliations. More precisely\, geometric prop erties of the foliation are translated into properties of the canonical bu ndle of the foliation. One of the most important invariants describing th e properties of a line bundle L is its Kodaira dimension kod(L)\, which m easures the growth of the global sections of L and its tensor powers. The Kodaira dimension of a foliation F is defined as the Kodaira dimension of its canonical bundle kod(KF). In their fundamental works\, Br unella and McQuillan give a classfication of foliations on surfaces on th e model of Enriques-Kodaira classification of surfaces. The next step is the study of the behaviour of families of foliations. Brunella proves tha t\, for a family of foliations (Xt\, Ft) of dimensio n one on surfaces\, satisfying certain hypotheses of regularity\, the Kod aira dimension of the foliation does not depend on t. By analogy with Si u's Invariance of Plurigenera\, it is natural to ask whether for a family of foliations (Xt\, Ft) the dimensions of global se ctions of the canonical bundle and its powers depend on t. In this talk w e will discuss to which extent an Invariance of Plurigenera for foliation s is true and under which hypotheses on the family of foliations it holds . DTEND;TZID=Europe/Zurich:20151030T120000 END:VEVENT BEGIN:VEVENT UID:news689@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230411 DTSTART;TZID=Europe/Zurich:20151023T103000 SUMMARY:Seminar Algebra and Geometry: Jakub Witaszek (Imperial College Lond on) DESCRIPTION:The famous Fujita conjecture says that KX + (d+2)A is very ampl e\, where X is a smooth projective variety of dimension d\, and A is an a mple divisor. Despite its simple statement\, the conjecture is only known for d < 3 in characteristic zero. In positive characteristic\, the conj ecture hasn't been even proved for surfaces\, but thanks to the recent pr ogress due to Di Cerbo and Fanelli\, we know that when X is a projective smooth surface there exist constants a\, b ∈ ℕ such that aKX + bA is very ample. In this talk\, we will discuss similar bounds in the case whe n X is singular. X-ALT-DESC: The famous Fujita conjecture says that KX + (d+2)A i s very ample\, where X is a smooth projective variety of dimension d\, an d A is an ample divisor. Despite its simple statement\, the conjecture is only known for d <\; 3 in characteristic zero. In positive characteris tic\, the conjecture hasn't been even proved for surfaces\, but thanks to the recent progress due to Di Cerbo and Fanelli\, we know that when X is a projective smooth surface there exist constants a\, b ∈ ℕ such tha t aKX + bA is very ample. In this talk\, we will discuss simil ar bounds in the case when X is singular. DTEND;TZID=Europe/Zurich:20151023T120000 END:VEVENT BEGIN:VEVENT UID:news688@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230425 DTSTART;TZID=Europe/Zurich:20151016T103000 SUMMARY:Seminar Algebra and Geometry: Arthur Renaudineau (Genève) DESCRIPTION:After recalling general problems in the study of topology of r eal algebraic varieties and Viro's method to construct such varieties\, w e will present a construction of real algebraic surfaces with many handle s in (CP1)3. X-ALT-DESC: After recalling general problems in the study of topology of&nb sp\;real algebraic varieties and Viro's method to construct such varieties \, \;we will present a construction of real algebraic surfaces with ma ny \;handles in \;(CP1)3.
 DTEND;TZID=Europe/Zurich:20151016T120000 END:VEVENT BEGIN:VEVENT UID:news687@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230438 DTSTART;TZID=Europe/Zurich:20151009T103000 SUMMARY:Seminar Algebra and Geometry: Jean-Philippe Furter (Basel) DESCRIPTION:The groups GL2(C[X1\,...\,Xm]) and Aut(An) can naturally be considered as ind-groups (algebraic groups of infinite dimension). As s uch\, they are endowed with the Zariski topology. We will describe severa l topological properties of these two groups. In particular\, we will giv e examples of closed subgroups. X-ALT-DESC: The groups \;GL2(C[X1\,...\,Xm]) \;and \;Aut(An) \;can naturally be considere d as ind-groups (algebraic groups of infinite dimension). \;As such\, they are endowed with the Zariski topology. We will describe several top ological properties of these two groups. In particular\, we will give exa mples of closed subgroups. DTEND;TZID=Europe/Zurich:20151009T120000 END:VEVENT BEGIN:VEVENT UID:news686@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230452 DTSTART;TZID=Europe/Zurich:20151002T103000 SUMMARY:Seminar Algebra and Geometry: Andrea Fanelli (Basel) DESCRIPTION:In this talk I will give a fast introduction to the problem of birational classification of algebraic varieties\, where Mori fibre spac es naturally appear. I will then discuss a classification project of the Fano varieties which can appear as a general fibre of a Mori fibre space (fibre-like Fano varieties). At this stage we have two criteria\, one suf ficient and one necessary\, to detect the fibre-likeness of a Fano variet y. These criteria turn into a characterisation in the rigid case. Our mai n applications are for surfaces\, three-folds and toric varieties. X-ALT-DESC: In this talk I will give a fast introduction to the problem of birational classification of algebraic varieties\, where Mori fibre spac es naturally appear. I will then discuss a classification project of the Fano varieties which can appear as a general fibre of a Mori fibre space (fibre-like Fano varieties). At this stage we have two criteria\, one suf ficient and one necessary\, to detect the fibre-likeness of a Fano variet y. These criteria turn into a characterisation in the rigid case. Our mai n applications are for surfaces\, three-folds and toric varieties. DTEND;TZID=Europe/Zurich:20151002T120000 END:VEVENT BEGIN:VEVENT UID:news685@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230504 DTSTART;TZID=Europe/Zurich:20150925T103000 SUMMARY:Seminar Algebra and Geometry: Ronan Terpereau (Bonn) DESCRIPTION:In this talk you will learn about Chevalley theorem for Lie alg ebras\, commuting scheme (associated with a Lie algebra\, a theta-group\, or a polar representation)\, symplectic reduction (associated with a re presentation of a reductive group)\, symplectic singularities and their r esolutions\, and about the beautiful relations between all these things. I will mention several questions remained open for decades and explained some recent approaches to try to answer them. This talk will be elementar y with many examples and shall provide a good opportunity to learn about representation theory of reductive groups and the Lie theory. X-ALT-DESC: In this talk you will learn about Chevalley theorem for Lie alg ebras\, commuting scheme (associated with a Lie algebra\, a theta-group\, or a polar representation)\, symplectic reduction (associated with a re presentation of a reductive group)\, symplectic singularities and their r esolutions\, and about the beautiful relations between all these things. I will mention several questions remained open for decades and explained some recent approaches to try to answer them. This talk will be elementar y with many examples and shall provide a good opportunity to learn about representation theory of reductive groups and the Lie theory. DTEND;TZID=Europe/Zurich:20150925T120000 END:VEVENT BEGIN:VEVENT UID:news684@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T230517 DTSTART;TZID=Europe/Zurich:20150918T103000 SUMMARY:Seminar Algebra and Geometry: Adrien Dubouloz (Dijon) DESCRIPTION:An exotic affine sphere is a smooth complex affine variety whic h is diffeomorphic to a smooth non degenerate affine quadric of the same dimension but not algebraically isomorphic to it. The smooth threefold w ith equation x2v + y2u = 1 is such an exotic sphere\, and in fact is esse ntially the unique example known so far. In this talk\, after a short rev iew of the existing results and open questions around these spheres\, I w ill discuss some strategies to construct larger families of exotic 3-sphe res\, as a well as higher dimensional exotic spheres. It time permits\, I will indicate some connexions between the exoticity of a certain 5-dimen sional sphere in the sens of A1-homotopy theory and the stable exoticity of the Russell cubic threefold. X-ALT-DESC: An exotic affine sphere is a smooth complex affine variety whic h is diffeomorphic to a smooth non degenerate affine quadric of the same dimension but not algebraically isomorphic to it. The smooth threefold w ith equation x2v + y2u = 1 is such an exotic sphere\ , and in fact is essentially the unique example known so far. In this tal k\, after a short review of the existing results and open questions aroun d these spheres\, I will discuss some strategies to construct larger fami lies of exotic 3-spheres\, as a well as higher dimensional exotic spheres . It time permits\, I will indicate some connexions between the exoticity of a certain 5-dimensional sphere in the sens of A1-homotopy theory and the stable exoticity of the Russell cubic threefold. DTEND;TZID=Europe/Zurich:20150918T120000 END:VEVENT BEGIN:VEVENT UID:news703@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T211242 DTSTART;TZID=Europe/Zurich:20150604T141500 SUMMARY:Seminar Algebra and Geometry: Joseph Landsberg (Texas A&M Universit y) DESCRIPTION:In 1969\, Strassen discovered the standard algorithm for multip lying two n×n matrices is not the optimal one. Subsequent work has led t o the astounding conjecture that as n goes to infinity it is nearly as ea sy to multiply matrices as it is to add them. I will explain uses of alg ebraic geometry\, differential geometry and representation theory in the study of this conjecture. X-ALT-DESC: In 1969\, Strassen discovered the standard algorithm for multip lying two n×n matrices is not the optimal one. Subsequent work has led t o the astounding conjecture that as n goes to infinity it is nearly as ea sy to multiply matrices as it is to add them. I will explain uses of alg ebraic geometry\, differential geometry and representation theory in the study of this conjecture. DTEND;TZID=Europe/Zurich:20150604T154500 END:VEVENT BEGIN:VEVENT UID:news702@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T210012 DTSTART;TZID=Europe/Zurich:20150529T103000 SUMMARY:Seminar Algebra and Geometry: Christian Urech (Universität Basel) DESCRIPTION:The Cremona group Crn of dimension n is the group of birational transformations of projective n-space. It is interesting to study group homomorphisms from Crn to Crm. However\, at the moment it seems to be ve ry difficult to find a general classification. In this talk I will recall some properties of Cr2 and define what an algebraic homomorphism between Cremona groups is. Then we will discuss in detail an example given by Gi zatullin of an embedding of Cr2 to Cr5 and some of its rich geometrical p roperties. X-ALT-DESC: The Cremona group Crn of dimension n is the group of birational transformations of projective n-space. It is interesting to s tudy group homomorphisms from Crn to Crm. However\, at the moment it seems to be very difficult to find a general classifica tion.

In this talk I will recall some properties of Cr2< /sub> and define what an algebraic homomorphism between Cremona groups is . Then we will discuss in detail an example given by Gizatullin of an emb edding of Cr2 to Cr5 and some of its rich geometric al properties. DTEND;TZID=Europe/Zurich:20150529T120000 END:VEVENT BEGIN:VEVENT UID:news701@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T205506 DTSTART;TZID=Europe/Zurich:20150522T103000 SUMMARY:Seminar Algebra and Geometry: Charlie Petitjean (Université de Bou rgogne) DESCRIPTION:In this talk we will consider birational equivalence of non nec essarily irreducible divisors on rational surfaces. It will be given an useful invariant (in this context) related to the Kodaira dimension. All the considered constructions will be connected to particular presentat ions of T-varieties. X-ALT-DESC: In this talk we will consider birational equivalence of non nec essarily irreducible divisors on rational surfaces. It will be given an useful invariant (in this context) related to the Kodaira dimension. All the considered constructions will be connected to particular presentat ions of T-varieties. DTEND;TZID=Europe/Zurich:20150522T120000 END:VEVENT BEGIN:VEVENT UID:news700@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T205023 DTSTART;TZID=Europe/Zurich:20150424T103000 SUMMARY:Seminar Algebra and Geometry: Mathieu Huruguen (EPFL\, Lausanne) DESCRIPTION:A linear algebraic group G defined over a field k is called spe cial if every G-torsor over every field extension of k is trivial. In a m odern language\, it can be shown that the special groups are those of esse ntial dimension zero. In 1958 Grothendieck classified special groups in t he case where the base field k is algebraically closed. In this talk I wi ll explain the classification of special reductive groups over an arbitrar y field. If time permits\, I will give an application to a conjecture of Serre. X-ALT-DESC: A linear algebraic group G defined over a field k is called spe cial if every G-torsor over every field extension of k is trivial. In a m odern language\, it can be shown that the special groups are those of esse ntial dimension zero. In 1958 Grothendieck classified special groups in t he case where the base field k is algebraically closed. In this talk I wi ll explain the classification of special reductive groups over an arbitrar y field. If time permits\, I will give an application to a conjecture of Serre. DTEND;TZID=Europe/Zurich:20150424T120000 END:VEVENT BEGIN:VEVENT UID:news699@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190202T205342 DTSTART;TZID=Europe/Zurich:20150410T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Universität Basel) DESCRIPTION:We show that the automorphism group of affinen-space An determi nes An up to isomorphism: If X is a connected affine variety such that Au t(X) \\simeq Aut(An) as ind-groups\, then X \\simeq An as varieties.We al so show that every torus appears as Aut(X) for a suitable affin e variety X\, but that Aut(X) cannot be isomorphic to a semisimpl e group. In fact\, if Aut(X) is finitedimensional and if X \\not\\ simeq A1\, then the connected component Aut(X)◦ is a torus.Concerning th e structure of Aut(An) we prove that any homomorphism Aut(An)→ G of ind- groups either factors through jac : Aut(An)→C∗ where jac is the Jacobi an determinant\, or it is a closed immersion. For SAut(An) := ker(jac)⊂ Aut(An) we show that everynontrivial homomorphism SAut(An)→G is a closed immersion.Finally\, we prove that every non-trivial homomorphism φ: SAu t(An)→SAut(An) is anautomorphism\, and that φ is given by conjugation w ith an element from Aut(An). X-ALT-DESC: We show that the automorphism group of affinen-space An determines An up to isomorphism: If X is a c onnected affine variety such that Aut(X) \\simeq Aut(An) as ind-groups\, then X \\simeq An as varieties.
We also show that every torus appears as Aut(X) for a suitable a ffine variety X\, but that Aut(X) cannot be isomorphic to a semis imple group. In fact\, if Aut(X) is finitedimensional and if X \\n ot\\simeq A1\, then the connected component Aut(X) ◦ is a torus.
Concerning the structure of Aut(An< /sup>) we prove that any homomorphism Aut(An)→ G of ind-groups either fa ctors through jac : Aut(An)→C∗ where jac is the Jacobian determinant\, or it is a closed immersion. For SAut(A< /b>n) := ker(jac)⊂Aut(An) we show that ever ynontrivial homomorphism SAut(An)→G is a closed immersion.
Finally\ , we prove that every non-trivial homomorphism φ: SAut(An)→SAut(An) is anautomorphism\, and that φ is given by conjugation with an element from Aut(An). DTEND;TZID=Europe/Zurich:20150410T120000 END:VEVENT BEGIN:VEVENT UID:news698@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190202T201415 DTSTART;TZID=Europe/Zurich:20150327T103000 SUMMARY:Seminar Algebra and Geometry: Pierre-Marie Poloni (Universität Bas el) DESCRIPTION:Explicit counterexamples to the Laurent Cancellation Problem X-ALT-DESC:Explicit counterexamples to the Laurent Cancellation Problem DTEND;TZID=Europe/Zurich:20150327T120000 END:VEVENT BEGIN:VEVENT UID:news697@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190202T201121 DTSTART;TZID=Europe/Zurich:20150320T103000 SUMMARY:Seminar Algebra and Geometry: Markus Hunziker (Baylor University\, Texas) DESCRIPTION:In this talk\, I will show how to solve several famous problems (old and new) from classical invariant theory by using the structure of c ertain categories of highest weight modules. For example\, the structure o f a category of highest weight modules for the symplectic Liealgebra sp2n( C) will be used to compute minimal free resolutions (syzygies) and Hilbert series of the modules of covariants for the action of the orthogonal group Ok(C) on Ck⊕···⊕Ck( n-copies). This in turn leads to a simple char acterization of the Cohen–Macaulaymodules of covariants. X-ALT-DESC: In this talk\, I will show how to solve several famous problems (old and new) from classical invariant theory by using the structure of c ertain categories of highest weight modules. For example\, the structure o f a category of highest weight modules for the symplectic Liealgebra sp2n(C) will be used to compute minimal free resolutions (syzygies) and Hilbertseries of the modules of covariants for the action of the ortho gonal group Ok(C) on Ck⊕···⊕Ck( n- copies). This in turn leads to a simple characterization of the Cohen–Ma caulaymodules of covariants. DTEND;TZID=Europe/Zurich:20150320T120000 END:VEVENT BEGIN:VEVENT UID:news696@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190202T200544 DTSTART;TZID=Europe/Zurich:20150313T103000 SUMMARY:Seminar Algebra and Geometry: Johan Björklund (Institut de Mathém atiques de Jussieu) DESCRIPTION:A real algebraic rational knot is an algebraic embedding of CP1 into CP3 by real polynomials. By applying a real projection to a (generi c) projective plane we obtain a real rational planar curve of the same d egree\, which should be thought of as the associated knot diagram (with a ppropriate decorations at double points). In classical smooth knot theory \, knots and their diagrams are closely interconnected. For each decorate d diagram\, there is a corresponding knot (constructed using an appropria te height-function). In the algebraic setting this does not hold true\, t here exists decorated real algebraic planar curves which can not be lifte d to an appropriate knot.In this talk I will explain how to associate a h yperplane arrangement to a nodal planar rational real algebraic curve. Th is arrangement describes the space of nonsingular liftings and allows us to calculate the homology (and thus\, in particular\, the number of lifti ngs up to rigid isotopy). We will show that\, up to degree 5\, this hyper plane arrangement is a rigid isotopy invariant (of planar curves) and can provide real algebraic analogues of the classical Reidemeister moves. Ob structions in the case of higher degrees will be discussed. The talk shou ld be accessible to nonspecialists. X-ALT-DESC: A real algebraic rational knot is an algebraic embedding of CP< sup>1 into CP3 by real polynomials. By applying a real p rojection to a (generic) projective plane we obtain a real rational plana r curve of the same degree\, which should be thought of as the associated knot diagram (with appropriate decorations at double points). In classic al smooth knot theory\, knots and their diagrams are closely interconnect ed. For each decorated diagram\, there is a corresponding knot (construct ed using an appropriate height-function). In the algebraic setting this d oes not hold true\, there exists decorated real algebraic planar curves w hich can not be lifted to an appropriate knot.

In this talk I will explain how to associate a hyperplane arrangement to a nodal planar rational real algebraic curve. This arrangement describes the space of n onsingular liftings and allows us to calculate the homology (and thus\, i n particular\, the number of liftings up to rigid isotopy). We will show that\, up to degree 5\, this hyperplane arrangement is a rigid isotopy in variant (of planar curves) and can provide real algebraic analogues of th e classical Reidemeister moves. Obstructions in the case of higher degree s will be discussed. The talk should be accessible to nonspecialists. DTEND;TZID=Europe/Zurich:20150313T120000 END:VEVENT BEGIN:VEVENT UID:news695@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190202T194348 DTSTART;TZID=Europe/Zurich:20150220T103000 SUMMARY:Seminar Algebra and Geometry: Jörg Winkelmann (Ruhr-Universität B ochum) DESCRIPTION:Conjecturally abundance of entire curves is closely related to abundance of rational points on projective varieties defined over a numbe r field.This is discussed in connection with algebraic groups and prinici pal bundles. More precisely\, let X be a projective manifold\, G an algeb raic group and E a G-principal bundle on X\, all defined over some number field K. Then E admits a Zariskidense set of L-rational points for some finite extension field iff X does. This corresponds to the homotopy lift ing property whose complex analytic analogue allows to lift entire curves . X-ALT-DESC: Conjecturally abundance of entire curves is closely related to abundance of rational points on projective varieties defined over a numbe r field.

This is discussed in connection with algebraic groups and prinicipal bundles. More precisely\, let X be a projective manifold\ , G an algebraic group and E a G-principal bundle on X\, all defined over some number field K. Then E admits a Zariski
dense set of L-rationa l points for some finite extension field iff X does. This corresponds to the homotopy lifting property whose complex analytic analogue allows to l ift entire curves. DTEND;TZID=Europe/Zurich:20150220T120000 END:VEVENT BEGIN:VEVENT UID:news716@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T232809 DTSTART;TZID=Europe/Zurich:20141219T103000 SUMMARY:Seminar Algebra and Geometry: Amos Turchet (Chalmers Universitet\, Göteborg) DESCRIPTION:Lang-Vojtas Conjectures are a set of deep and far reaching conj ectures\, formulated by Paul Vojta using ideas of Lang\, which embrace the distribution of solutions to Diophantine equations over number fields\, t he behaviour of holomorphic maps into complex manifolds and of algebraic c urves into algebraic varieties. In the (split) function field case the co njecture predicts (weak) algebraic hyperbolicity for log-general type vari eties.When the completion of the variety is the projective plane the conje cture is known both if the divisor at infinity consits of four lines in ge neral position (Brownawell-Masser and\,independently\, Voloch) and for a c onic and two lines with five singular points (Corvaja and Zannier). With different methods Chen and Pacienza-Rousseau proved that the conjecture ho lds in the hyperbolic case\, i.e. the complement of a very generic curve of degree at least 5.In the talk\, after an introduction to this fascinati ng subject\, we will show how to prove the conjecture in general for the c omplement of a very generic curve of degree at least four.The proof relies on a deformation argument applied to a conic and two lines and on the the ory of logarithmic stable maps as defined by Abramovich-Chen (and independ ently by Gross and Siebert) which extends usual stable maps to the logarit hmic category (in the sense of Kato and Illusie). X-ALT-DESC: Lang-Vojtas Conjectures are a set of deep and far reaching conj ectures\, formulated by Paul Vojta using ideas of Lang\, which embrace the distribution of solutions to Diophantine equations over number fields\, t he behaviour of holomorphic maps into complex manifolds and of algebraic c urves into algebraic varieties.
In the (split) function field case the conjecture predicts (weak) algebraic hyperbolicity for log-general typ e varieties.When the completion of the variety is the projective plane the conjecture is known both if the divisor at infinity consits of four lines in general position (Brownawell-Masser and\,independently\, Voloch) and f or a conic and two lines with five singular points (Corvaja and Zannier). With different methods Chen and Pacienza-Rousseau proved that the conject ure holds in the hyperbolic case\, i.e. the complement of a very generic curve of degree at least 5.
In the talk\, after an introduction to th is fascinating subject\, we will show how to prove the conjecture in gener al for the complement of a very generic curve of degree at least four.The proof relies on a deformation argument applied to a conic and two lines an d on the theory of logarithmic stable maps as defined by Abramovich-Chen ( and independently by Gross and Siebert) which extends usual stable maps to the logarithmic category (in the sense of Kato and Illusie). DTEND;TZID=Europe/Zurich:20141219T120000 END:VEVENT BEGIN:VEVENT UID:news715@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T232307 DTSTART;TZID=Europe/Zurich:20141212T103000 SUMMARY:Seminar Algebra and Geometry: Salomon Vishkautsan (ERC postdoc at S cuola Normale Superiore di Pisa) DESCRIPTION:In this talk we present a local-global property in arithmetic d ynamics called strong residual periodicity\, as defined by Bandman\, Grune wald and Kunyavskii in 2010. We start with a dynamical system induced by an endomorphism of a quasi projective variety defined over a number field. This system can be reduced mod p for “almost all” primes in the ring of integers of the number field. We can then ask how the dy namics of the global system relate to the dynamics of the system reduce d mod p for almost all primes p. Strong residual periodicity occurs when points of small period exist modulo almost every prime\,but “cannot be e xplained” by the dynamics of the global system. The aim of this talk is to present many motivating examples and raise some interesting questions to encourage further research on this topic. X-ALT-DESC: In this talk we present a local-global property in arithmetic d ynamics called strong residual periodicity\, as defined by Bandman\ , Grunewald and Kunyavskii in 2010. We start with a dynamical system indu ced by an endomorphism of a quasi projective variety defined over a number field. This system can be reduced mod p for “almost all” primes in t he ring of integers of the number field. We can then ask how the dynamics of the global system relate to the dynamics of the system reduced mod p for almost all primes p. Strong residual periodicity occur s when points of small period exist modulo almost every prime\,but “cann ot be explained” by the dynamics of the global system. The aim of this talk is to present many motivating examples and raise some interesting que stions to encourage further research on this topic. DTEND;TZID=Europe/Zurich:20141212T120000 END:VEVENT BEGIN:VEVENT UID:news714@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T231842 DTSTART;TZID=Europe/Zurich:20141205T103000 SUMMARY:Seminar Algebra and Geometry: Eric Edo (Université de la Nouvelle Calédonie) DESCRIPTION:Joint work with S. Kuroda\\r\\nGiven a domain R of characterist ic p >0\, there exist two subgroups of the group GAn(R) of polynomial auto morphisms which are natural generalisations of the linear group GLn(R).\\r \\n1) The subgroup of additive automorphisms\, i.e. automorphisms with n components satisfying f(x+y) =f(x)+f(y) where x and y are set of n variabl es.\\r\\n2) The subgroup of automorphisms with a Jacobian matrix in GLn(R) .\\r\\nThe subgroup generated by the translations and automorphisms of the type 1 (resp. 2) is called geometrically affine (resp. differentially a ffine). This group\, together with the triangular automorphisms\, generat es the subgroup of geometrically tame (resp. differentially tame) automor phisms. We study these groups in dimension 2. We prove that they are dif ferent and endowed with a nice structure of amalgamated product. X-ALT-DESC: Joint work with S. Kuroda\nGiven a domain R of characteristic p >\;0\, there exist two subgroups of the group GAn(R) of polynomial auto morphisms which are natural generalisations of the linear group GLn(R).\n1) The subgroup of additive automorphisms\, i.e. automorphisms with n components satisfying f(x+y) =f(x)+f(y) where x and y are set of n variables.\n2) The subgroup of automorphisms with a Jacobian matrix in GL< sub>n(R).\nThe subgroup generated by the translations and automorphi sms of the type 1 (resp. 2) is called geometrically affine (resp. differ entially affine). This group\, together with the triangular automorphisms \, generates the subgroup of geometrically tame (resp. differentially tam e) automorphisms. We study these groups in dimension 2. We prove that th ey are different and endowed with a nice structure of amalgamated product. DTEND;TZID=Europe/Zurich:20141205T120000 END:VEVENT BEGIN:VEVENT UID:news713@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T231253 DTSTART;TZID=Europe/Zurich:20141128T103000 SUMMARY:Seminar Algebra and Geometry: Donna Testerman (EPFL\, Lausanne) DESCRIPTION:In joint work with Ross Lawther\, and building on work of Proud and Seitz\, we considered properties of CG(CG(u)) =Z(CG(u))\, where G is a simple algebraic group defined over an algebraically closed field of goo d positive characteristic or of characteristic 0\, and u is a unipotent el ement. In particular\, we determined the dimension of the double centrali zer.In subsequent work\, Simion considered the case of bad characteristic\ , and determined the dimension for G of exceptional type.We discuss the ab ove work\, describe the results and in particular\, indicate the differenc es between good and bad characteristic. Furthermore\, in the case where t he characteristic is good or 0 and u is an even element (that is\, the ass ociated cocharacter has even weights on Lie(G))\, there is a particularly nice formula for this dimension. We indicate a recent case-free proof o f one of the inequalities implied by this formula\, obtained by myself in characteristic 0 and in collaboration with McNinch in positive characteristic. X-ALT-DESC: In joint work with Ross Lawther\, and building on work of Proud and Seitz\, we considered properties of CG(CG(u)) = Z(CG(u))\, where G is a simple algebraic group defined over an algebraically closed field of good positive characteristic or of character istic 0\, and u is a unipotent element. In particular\, we determined the dimension of the double centralizer.In subsequent work\, Simion considere d the case of bad characteristic\, and determined the dimension for G of e xceptional type.We discuss the above work\, describe the results and in pa rticular\, indicate the differences between good and bad characteristic. Furthermore\, in the case where the characteristic is good or 0 and u is a n even element (that is\, the associated cocharacter has even weights on L ie(G))\, there is a particularly nice formula for this dimension. We indi cate a recent case-free proof of one of the inequalities implied b y this formula\, obtained by myself in characteristic 0 and in colla boration with McNinch in positive characteristic. DTEND;TZID=Europe/Zurich:20141128T120000 END:VEVENT BEGIN:VEVENT UID:news712@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T230735 DTSTART;TZID=Europe/Zurich:20141121T103000 SUMMARY:Seminar Algebra and Geometry: Alberto Calabri (Università di Ferra ra) DESCRIPTION:A plane curve C is said to be Cremona contractible if there exi sts a plane Cremona transformation that contracts C to a point. A charac terization of irreducible plane curves which are Cremona contractible is a classical result due to Castelnuovo and Enriques in 1900 and that has b een improved by Kumar and Murthy in 1982. The case of two irreducible com ponents is due to Iitaka in 1988. After reviewing these results\, we will discuss the open problem of characterizing reducible (reduced) plane cur ves which are Cremona contractible. In particular we will deal with reduc ed unions of lines and we will give a classification in case the lines ar e at least 12.This is a joint work in progress with Ciro Ciliberto (Univ. Roma "Tor Vergata"). X-ALT-DESC: A plane curve C is said to be Cremona contractible if there exi sts a plane Cremona transformation that contracts C to a point. A charac terization of irreducible plane curves which are Cremona contractible is a classical result due to Castelnuovo and Enriques in 1900 and that has b een improved by Kumar and Murthy in 1982. The case of two irreducible com ponents is due to Iitaka in 1988. After reviewing these results\, we will discuss the open problem of characterizing reducible (reduced) plane cur ves which are Cremona contractible. In particular we will deal with reduc ed unions of lines and we will give a classification in case the lines ar e at least 12.

This is a joint work in progress with Ciro Cilib erto (Univ. Roma "\;Tor Vergata"\;). DTEND;TZID=Europe/Zurich:20141121T120000 END:VEVENT BEGIN:VEVENT UID:news711@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T230340 DTSTART;TZID=Europe/Zurich:20141114T103000 SUMMARY:Seminar Algebra and Geometry: Immanuel Stampfli (Jacobs University\ , Bremen) DESCRIPTION:This is joint work with Peter Feller (University of Bern). Let X be a smooth affine algebraic variety. A natural question is\, whe ther two algebraic embeddings f\, g : X → Cm are algebraically equiva lent\, i.e. whether there exists an algebraic automorphism φ of Cm such that φ◦f=g. Kaliman\, Nori and Srinivas gave an affirmative an swer\, provided that 2 dimX+ 2≤m. In this talk we discuss the followi ng one-dimensional improvement under a relaxed equivalence condition.\\r\\ nTheorem. If f\, g : X → Cm are algebraic embeddings and 2 dimX+ 1≤m\, then there exists a holomorphic automorphism φ of Cm such that φ◦f=g. \\r\\nIn fact\, the proof is based on an idea of Kaliman\, with which he proved that two algebraic embeddings of C into C3 are holom orphically equivalent. In the course of this talk\, we discuss this idea . Moreover\, we provide examples of algebraic embeddings into Cm that ar e holomorphically non-equivalent. X-ALT-DESC: This is joint work with Peter Feller (University of Bern). Let X be a smooth affine algebraic variety. A natural question is\, whe ther two algebraic embeddings f\, g : X → Cm are al gebraically equivalent\, i.e. whether there exists an algebraic automorph ism φ of Cm such that φ◦f=g. Kaliman\, Nori and Srinivas gave an affirmative answer\, provided that 2 dimX+ 2≤m. In this talk we discuss the following one-dimensional improvement under a relaxed equivalence condition.\nTheorem. If f\, g : X → Cm< /sup> are algebraic embeddings and 2 dimX+ 1≤m\, then there exists a hol omorphic automorphism φ of Cm such that φ◦f=g.\nIn fact\, the proof is based on an idea of Kaliman\, with which h e proved that two algebraic embeddings of C into C3< /sup> are holomorphically equivalent. In the course of this talk\, we di scuss this idea. Moreover\, we provide examples of algebraic embeddings into Cm that are holomorphically non-equivalent. DTEND;TZID=Europe/Zurich:20141114T120000 END:VEVENT BEGIN:VEVENT UID:news710@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T225437 DTSTART;TZID=Europe/Zurich:20141107T103000 SUMMARY:Seminar Algebra and Geometry: Jung Kyu Canci (Universität Basel) DESCRIPTION:Let K be a number field and v a non archimedean valuatio n on K. We say that an endomorphism Φ : P1 → P1\, defined over K\, has good reduction at v if there exists a model Ψ for Φ such that deg Ψv\, the degree of the reduction of Ψ modulo v\, equals deg Ψ . We will present a criteria for the good reduction that is a generalizati on of a similar result due to Zannier where he considered some particular Belyi coverings (i.e. unramified except above{0\,1\,∞}). Our result ap plies to any rational maps and is in connection with other two notions of good reduction\, the simple and the critically good reduction. X-ALT-DESC: Let K be a number field and v a non archimedean valuatio n on K. We say that an endomorphism Φ : P1 → P1\, defined over K\, has good reduction at v if there exists a model Ψ for Φ such that deg Ψv\, the degree of the reduction of Ψ modulo v\, equals deg Ψ . We will present a criteria for the good reduction that is a generalizati on of a similar result due to Zannier where he considered some particular Belyi coverings (i.e. unramified except above{0\,1\,∞}). Our result ap plies to any rational maps and is in connection with other two notions of good reduction\, the simple and the critically good reduction. DTEND;TZID=Europe/Zurich:20141107T120000 END:VEVENT BEGIN:VEVENT UID:news709@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T224849 DTSTART;TZID=Europe/Zurich:20141031T103000 SUMMARY:Seminar Algebra and Geometry: Alexandre Ramos Peon (Universität Be rn) DESCRIPTION:As has been discussed recently in this seminar\, manifolds with the "density property" have a particularly rich group of holomorphic au tomorphisms. In particular this group acts infinite-transitively on the m anifold. This can be generalized as follows: if instead of this static st ate\, we allow the configuration of finitely many points to vary in a hol omorphic fashion\, then there exists a "holomorphically depending" family of automorphisms\, mapping\, for each parameter\, the corresponding conf iguration to a pre-defined tuple of points on the manifold. This is not t rivial even in the affine case. The aim of the talk is to  introduce the notions and tools required\, and of course to sketch a proof of a precis e version of this theorem. X-ALT-DESC: As has been discussed recently in this seminar\, manifolds with the "\;density property"\; have a particularly rich group of hol omorphic automorphisms. In particular this group acts infinite-transitive ly on the manifold. This can be generalized as follows: if instead of thi s static state\, we allow the configuration of finitely many points to va ry in a holomorphic fashion\, then there exists a "\;holomorphically depending"\; family of automorphisms\, mapping\, for each parameter\, the corresponding configuration to a pre-defined tuple of points on the manifold. This is not trivial even in the affine case. The aim of the ta lk is to \; introduce the notions and tools required\, and of course t o sketch a proof of a precise version of this theorem. DTEND;TZID=Europe/Zurich:20141031T120000 END:VEVENT BEGIN:VEVENT UID:news708@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T224457 DTSTART;TZID=Europe/Zurich:20141024T103000 SUMMARY:Seminar Algebra and Geometry: Jérémy Blanc (Universität Basel) DESCRIPTION:Over an algebraically closed field\, the conjugacy classes of the groups GLn and SLn are well-known. In particular\, an element is diag onalisable if and only if its conjugacy class is closed. The same res ult holds for polynomial automorphisms of the complex plane (Furte r-Maubach). In this talk\, I will present the case of the subg roup of polynomial automorphisms of the affine space of Jacobian 1 (anal ogue of SLn)\, which behaves very differently\, especially in dimension 2 . X-ALT-DESC: Over an algebraically closed field\, the conjugacy classes of the groups GLn and SLn are well-known. In particula r\, an element is diagonalisable if and only if its conjugacy class is cl osed. The same result holds for polynomial automorphisms of the complex plane (Furter-Maubach). In this talk\, I will present th e case of the subgroup of polynomial automorphisms of the affine spa ce of Jacobian 1 (analogue of SLn)\, which behaves very differ ently\, especially in dimension 2. DTEND;TZID=Europe/Zurich:20141024T120000 END:VEVENT BEGIN:VEVENT UID:news707@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T223920 DTSTART;TZID=Europe/Zurich:20141010T103000 SUMMARY:Seminar Algebra and Geometry: Matthias Leuenberger (Universität Be rn) DESCRIPTION:The hypersurface X given by x2y+x+z2+t3 = 0 is called Koras-Ru ssell cubic threefold and it played an important role in affine algebraic geometry. It is an example of a threefold that is diffeomorphic to R6 bu t not isomorphic to C3 as an algebraic variety. The latter statement foll ows from the fact that the Makar-Limanov invariant is non-trivial\, which means that there is a lack of algebraic automorphisms compared with C3. However\, in the holomorphic setting the situation is completely differen t: We will see that there are significantly more holomorphic autmorphisms on the Koras-Russel cubic X than algebraic ones. In fact the holomorphic automorphisms act transitively on the cubic. Actually X even has the dens ity property\, which means that the group of holomorphic automorphisms is in some sense huge. The question if X is biholomorphic to C3 is still open . X-ALT-DESC: The hypersurface X given by x2y+x+z2+t3 = 0 is called Koras-Russell cubic threefold and it playe d an important role in affine algebraic geometry. It is an example of a t hreefold that is diffeomorphic to R6 but not isomorphic to C3 as an algebraic variety. The latter statement fo llows from the fact that the Makar-Limanov invariant is non-trivial\, whi ch means that there is a lack of algebraic automorphisms compared with C3. However\, in the holomorphic setting the situation is completely different: We will see that there are significantly more holo morphic autmorphisms on the Koras-Russel cubic X than algebraic on es. In fact the holomorphic automorphisms act transitively on the cubic. A ctually X even has the density property\, which means that the grou p of holomorphic automorphisms is in some sense huge. The question if X is biholomorphic to C3 is still open. DTEND;TZID=Europe/Zurich:20141010T120000 END:VEVENT BEGIN:VEVENT UID:news706@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T223523 DTSTART;TZID=Europe/Zurich:20141003T103000 SUMMARY:Seminar Algebra and Geometry: Frank Kutzschebauch (Universität Ber n) DESCRIPTION:Compared to the real differentiable case complex manifolds in g eneral are more rigid\, their groups of holomorphic diffeomorphisms are ra ther small (in general trivial). A long known exception to this behavior is affine n-space Cn for n at least 2\, its group of holomorphic diffeomor phisms is infinite dimensional. In the late 1980’s Andersen - Lempert p roved are markable theorem which stated in its generalized version due to Forstneric and Rosay that any local holomorphic phase flow given on a Rung e subset ofCncan be locally uniformly approximated by a global holomorphic diffeomorphism. The main ingredient in the proof was formalized by Varol in to be called the density property: The Lie algebra generated by comple te holomorphic vector fields is dense in the Lie algebra of all holomorphi c vector fields. In these manifolds a similar local to global ap proximation of Andersen-Lempert type holds\, It is a precise way of sayi ng that the group of holomorphic diffeomorphisms is large. In the talk we will explain how this notion is related to other more recent flexibility notions in Complex Geometry\, in particular to the notion of Oka-Forstneri c manifold. We will give examples of manifolds with the density property and sketch applications of the density property. If time permits we will explain criteria for the density property developed by Kaliman and the spe aker or sketch some future plans. X-ALT-DESC: Compared to the real differentiable case complex manifolds in g eneral are more rigid\, their groups of holomorphic diffeomorphisms are ra ther small (in general trivial). A long known exception to this behavior is affine n-space Cn for n at least 2\, its group of hol omorphic diffeomorphisms is infinite dimensional. In the late 1980’s An dersen - Lempert proved are markable theorem which stated in its generaliz ed version due to Forstneric and Rosay that any local holomorphic phase fl ow given on a Runge subset ofCncan be locally uniformly approximated by a global holomorphic diffeomorphism. The main ingredient in the proof was f ormalized by Varolin to be called the density property: The Lie algebra g enerated by complete holomorphic vector fields is dense in the Lie algebra of all holomorphic vector fields. In these manifolds a similar loc al to global approximation of Andersen-Lempert type holds\, It is a p recise way of saying that the group of holomorphic diffeomorphisms is larg e. In the talk we will explain how this notion is related to other more r ecent flexibility notions in Complex Geometry\, in particular to the notio n of Oka-Forstneric manifold. We will give examples of manifolds with the density property and sketch applications of the density property. If tim e permits we will explain criteria for the density property developed by K aliman and the speaker or sketch some future plans. DTEND;TZID=Europe/Zurich:20141003T120000 END:VEVENT BEGIN:VEVENT UID:news705@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T212326 DTSTART;TZID=Europe/Zurich:20140926T103000 SUMMARY:Seminar Algebra and Geometry: Adrien Dubouloz (Université de Bourg ogne) DESCRIPTION:A much less studied version of Zariski Cancellation Problem ask s whether two algebraic varieties which become isomorphic after taking t heir products with an affine algebraic torus are isomorphic themselves. It is easy to see that the answer is positive when the two varieties ar e smooth algebraic curves. For higher dimensional varieties\, the proble m is more subtle\, intimately related to the geometry of families of af fine rational curves on them. The only available general result so far i s that "cancellation" holds provided that one the two varieties is not d ominantly covered by images of the punctured affine line\, a property sa tisfied for instance by varieties of log-general type. After a brief sur vey of various aspects of the problem\, I will present some strategies to construct smooth affine factorial counter-examples to cancellation in any dimension bigger or equal to two. X-ALT-DESC: A much less studied version of Zariski Cancellation Problem ask s whether two algebraic varieties which become isomorphic after taking t heir products with an affine algebraic torus are isomorphic themselves. It is easy to see that the answer is positive when the two varieties ar e smooth algebraic curves. For higher dimensional varieties\, the proble m is more subtle\, intimately related to the geometry of families of af fine rational curves on them. The only available general result so far i s that "\;cancellation"\; holds provided that one the two varieti es is not dominantly covered by images of the punctured affine line\, a property satisfied for instance by varieties of log-general type. After a brief survey of various aspects of the problem\, I will present some strategies to construct smooth affine factorial counter-examples to canc ellation in any dimension bigger or equal to two. DTEND;TZID=Europe/Zurich:20140926T120000 END:VEVENT BEGIN:VEVENT UID:news704@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190207T211858 DTSTART;TZID=Europe/Zurich:20140919T103000 SUMMARY:Seminar Algebra and Geometry: Ronan Terpereau (Universität Mainz) DESCRIPTION:This talk focuses on a work initiated by Tanja Becker in her Ph D thesis three years ago and completed recently by myself.\\r\\nGiven a r eductive group G acting on an affine scheme X\, a Hilbert function h\, an d a stability condition θ\, we explain how to construct the moduli space M of θ-stable (G\,h)-constellations on X\, which is a common generaliza tion of the invariant Hilbert scheme after Alexeev and Brion and of the m oduli space of θ-stable G-constellations for finite groups introduced by Craw and Ishii. The main tools for this construction are the geometric i nvariant theory and the invariant Quot schemes. Moreover\, the moduli spa ce M is naturally equipped with a morphism μ: M → X//G which turns to be a “nice” desingularization of the quotient X//G in many situation s. X-ALT-DESC:This talk focuses on a work initiated by Tanja Becker in her PhD thesis three years ago and completed recently by myself.\nGiven a reduct ive group G acting on an affine scheme X\, a Hilbert function h\, and a s tability condition θ\, we explain how to construct the moduli space M of θ-stable (G\,h)-constellations on X\, which is a common generalization of the invariant Hilbert scheme after Alexeev and Brion and of the moduli space of θ-stable G-constellations for finite groups introduced by Craw and Ishii. The main tools for this construction are the geometric invari ant theory and the invariant Quot schemes. Moreover\, the moduli space M is naturally equipped with a morphism μ: M \;→ X//G which turns to be a “nice” desingularization of the quotient X//G in many situation s. DTEND;TZID=Europe/Zurich:20140919T120000 END:VEVENT BEGIN:VEVENT UID:news717@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T181031 DTSTART;TZID=Europe/Zurich:20140523T103000 SUMMARY:Seminar Algebra and Geometry: Maria Fernanda Robayo (Universität Basel) DESCRIPTION:A birational diffeomorphism of a real projective algebraic vari ety X is a birational map that restricts to a diffeomorphism on the real p oints of X. In my talk\, X will be the sphere\, that is\, the projective a lgebraic surface defined by x2+y2+z2=w2 in P3R endowed with the complex c onjugation\, which gives it its real structure. The systematic investigat ion of real algebraic surfaces has already begun with Comessatti in 1912. On the other hand\, their automorphisms\, the birational diffeomorphisms \, have not been classified up to now. I will give an introduction into t he subject and present the complete classification of birational diffeomo rphisms of the sphere of prime order. X-ALT-DESC: A birational diffeomorphism of a real projective algebraic vari ety X is a birational map that restricts to a diffeomorphism on the real points of X. In my talk\, X will be the sphere\, that is\, the projective algebraic surface defined by x2+y2+z2=w2 in P3R endowed with the complex conjugation\, which gives it its real structure. The systemat ic investigation of real algebraic surfaces has already begun with Comess atti in 1912. On the other hand\, their automorphisms\, the birational di ffeomorphisms\, have not been classified up to now. I will give an introd uction into the subject and present the complete classification of birati onal diffeomorphisms of the sphere of prime order. DTEND;TZID=Europe/Zurich:20140523T120000 END:VEVENT BEGIN:VEVENT UID:news718@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T181323 DTSTART;TZID=Europe/Zurich:20140520T110000 SUMMARY:Seminar Algebra and Geometry: Yuri Prokhorov (Steklov Mathematical Institute) DESCRIPTION:A group B is said to be Jordan if there is a constant J=J(B) su ch that if for any finite subgroup G ⊂ B there exists a normal abelian s ubgroup A ⊂ G of index at most J. We discuss the following natural probl em: describe algebraic varieties for which the group of  birational self- maps is Jordan. X-ALT-DESC: A group B is said to be Jordan if there is a constant J=J(B) such that if for any finite subgroup G ⊂ B there exists a normal abelian subgroup A ⊂ G of index at most J. We discuss the following natural problem: descr ibe algebraic varieties for which the group of \; birational self-maps is Jordan. DTEND;TZID=Europe/Zurich:20140520T120000 END:VEVENT BEGIN:VEVENT UID:news719@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T181650 DTSTART;TZID=Europe/Zurich:20140509T103000 SUMMARY:Seminar Algebra and Geometry: Kevin Langlois (Institut Fourier\, Gr enoble) DESCRIPTION:This talk is devoted to the classification of normalized additi ve group actions on affine spherical varieties. After recalling some basi c notions concerning the Luna-Vust theory\, we will present a description of these actions which generalizes the classical toric case. Joint work with Alexander Perepechko. X-ALT-DESC: This talk is devoted to the classification of normalized additi ve group actions on affine spherical varieties. After recalling some basi c notions concerning the Luna-Vust theory\, we will present a description of these actions which generalizes the classical toric case.
Joint work with Alexander Perepechko. DTEND;TZID=Europe/Zurich:20140509T120000 END:VEVENT BEGIN:VEVENT UID:news720@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T182549 DTSTART;TZID=Europe/Zurich:20140502T103000 SUMMARY:Seminar Algebra and Geometry: Vincent Emery (EPFL) DESCRIPTION:I will recall the classical constructions for hyperbolic manifo lds of finite volume\, and in particular the method based on arithmetic g roups. I will then discuss a conjecture that states that except in dimens ion n=3\, the complete hyperbolic n-manifold of the smallest volume is n oncompact (joint work with Misha Belolipetsky). X-ALT-DESC: I will recall the classical constructions for hyperbolic manifo lds of finite volume\, and in particular the method based on arithmetic g roups. I will then discuss a conjecture that states that except in dimens ion n=3\, the complete hyperbolic n-manifold of the smallest volume is n oncompact (joint work with Misha Belolipetsky). DTEND;TZID=Europe/Zurich:20140502T120000 END:VEVENT BEGIN:VEVENT UID:news721@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T182835 DTSTART;TZID=Europe/Zurich:20140425T103000 SUMMARY:Seminar Algebra and Geometry: Ivan Bazhov (Univesité de Genève) DESCRIPTION:Let X be an affine toric variety and Aut(X) be its automorphism group. In the first part of the talk we give a combinatorial description of Aut(X)-orbits on X in terms of the divisor class group Cl(X). In the se cond part we introduce the total coordinates on X. The total coordinate ri ng provides a canonical presentation $\\overline{X}$ → X of X as a quo tient of a vector space $\\overline{X}$ by a linear action of a quasitoru s. We show that the orbits of the connected component of the group Aut(X) on X coincide with the Luna strata defined by the canonical quotient pres entation. X-ALT-DESC: Let X be an affine toric variety and Aut(X) be it s automorphism group. In the first part of the talk we give a combinatoria l description of Aut(X)-orbits on X in terms of the divisor class group Cl(X).
In the second part we introduce the total coordinates on X. The total coordinate ring provides a canonical pr esentation $\\overline{X}$ → X \;of X as a quotient o f a vector space $\\overline{X}$ by a linear action of a quasitorus. We s how that the orbits of the connected component of the group Aut(X) on X coincide with the Luna strata defined by the canonical quotie nt presentation. DTEND;TZID=Europe/Zurich:20140425T120000 END:VEVENT BEGIN:VEVENT UID:news722@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T183121 DTSTART;TZID=Europe/Zurich:20140411T103000 SUMMARY:Seminar Algebra and Geometry: Andriy Regeta (Universität Basel) DESCRIPTION:We show that every Lie algebra automorphisms of the vector fiel ds VF(An) of affine n-space An\, of the vector fields VFc(An) with constan t divergence\, and of the vector fields VF0(An) with divergence zero is in duced by an automorphism of An. As an immediate consequence\, we get the f ollowing result due to Kulikov. If every injective endomorphism of the Lie algebra VF(An) is an automorphism\, then the Jacobian Conjecture holds in dimension n. X-ALT-DESC: We show that every Lie algebra automorphisms of the vector fiel ds VF(An) of affine n-space An\, of th e vector fields VFc(An) with constant diverge nce\, and of the vector fields VF0(An) with d ivergence zero is induced by an automorphism of An.

As an immediate consequence\, we get the following result due to K ulikov. If every injective endomorphism of the Lie algebra VF(An) is an automorphism\, then the Jacobian Conjecture holds in dimen sion n. DTEND;TZID=Europe/Zurich:20140411T120000 END:VEVENT BEGIN:VEVENT UID:news724@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T185003 DTSTART;TZID=Europe/Zurich:20140321T103000 SUMMARY:Seminar Algebra and Geometry: Jung Kyu Canci (Universität Basel) DESCRIPTION:I will present a joint work with Laura Paladino. \\r\\nWe con sider dynamical systems on the projective line given by rational functio ns. Let $\\phi$ be an endomorphism of the projective line defined over a global field K. We prove a bound for the cardinality of the set of K-r ational preperiodic points for $\\phi$ in terms of the number of places of bad reduction. The result is completely new in the function fields c ase and it is an improvement of the number fields case. An important too l is an S-unit equation theorem in 2 variables. X-ALT-DESC:I will present a joint work with Laura Paladino. \nWe consider dynamical systems on the projective line given by rational functions. L et \;$\\phi$ be an endomorphism of the projective line defined over a global field K. We prove a bound for the cardinality of the set of K-r ational preperiodic points for $\\phi$ in terms of the number of places of bad reduction. The result is completely new in the function fields c ase and it is an improvement of the number fields case. An important too l is an S-unit equation theorem in 2 variables. DTEND;TZID=Europe/Zurich:20140321T120000 END:VEVENT BEGIN:VEVENT UID:news725@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T184751 DTSTART;TZID=Europe/Zurich:20140307T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Universität Basel) DESCRIPTION:Closed ind-subgroups with the same Lie algebras X-ALT-DESC:Closed ind-subgroups with the same Lie algebras DTEND;TZID=Europe/Zurich:20140307T120000 END:VEVENT BEGIN:VEVENT UID:news726@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T184914 DTSTART;TZID=Europe/Zurich:20140228T103000 SUMMARY:Seminar Algebra and Geometry: Pierre-Marie Poloni (Universität Bas el) DESCRIPTION:The tame automorphism group of affine 3-space is not closed X-ALT-DESC:The tame automorphism group of affine 3-space is not closed DTEND;TZID=Europe/Zurich:20140228T120000 END:VEVENT BEGIN:VEVENT UID:news727@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T201430 DTSTART;TZID=Europe/Zurich:20131220T103000 SUMMARY:Seminar Algebra and Geometry: Rafael Tiedra (Pontificia Universidad Católica de Chile) DESCRIPTION:Let X and G be compact Lie groups\, F1: X → X the time-one ma p of a C∞ measure-preserving flow\, φ: X → G a continuous function an d π a finite-dimensional irreducible unitary representation of G. Then\, we prove that the skew productsTφ:X x G → X x G\,  (x\,g) → (F1(x)\ , gφ(x))\,have purely absolutely continuous spectrum in the subspace asso ciated to π if ποφ has a Dini-continuous Lie derivative along the flow and if a matrix multiplication operator related to the topological degree of ποφ has nonzero determinant. This result provides a simple\, but ge neral\, criterion for the presence of an absolutely continuous component i n the spectrum of skew products of compact Lie groups. X-ALT-DESC: Let X and G be compact Lie groups\, F 1: X → X the time-one map of a C∞ measure-pres erving flow\, φ: X → G a continuous function and π \;a finite-dimensional irreducible unitary representation of G. Then\, we prove that the skew products

Tφ:X < /i>x G → X x G\, \; (x\,g) → (< i>F1(x)\, gφ(x))\,

have pu rely absolutely continuous spectrum in the subspace associated to π if ποφ has a Dini-continuous Lie derivative along the f low and if a matrix multiplication operator related to the topological deg ree of ποφ has nonzero determinant. This result provides a simple\, but general\, criterion for the presence of an absolutely conti nuous component in the spectrum of skew products of compact Lie groups. DTEND;TZID=Europe/Zurich:20131220T120000 END:VEVENT BEGIN:VEVENT UID:news728@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T201639 DTSTART;TZID=Europe/Zurich:20131122T103000 SUMMARY:Seminar Algebra and Geometry: Andriy Regeta (Universität Basel) DESCRIPTION:We study Lie subalgebras L of the vector fields Vecc(A2) of aff ine 2-space A2 of constant divergence\, and we classify those L which are isomorphic to the Lie algebra aff2 of the group Aff2(K) of affine transfor mations of A2. We then show that the following statements are equivalent:( a) The Jacobian Conjecture holds in dimension 2\;(b) All Lie subalgebras L ⊂ Vecc(A2) isomorphic to aff2 are conjugate under Aut(A2)\;(c) All Lie subalgebras L ⊂ Vecc(A2) isomorphic to aff2 are algebraic. X-ALT-DESC: We study Lie subalgebras L of the vector fields Vecc (A2) of affine 2-space A2 of constant divergence\, and we classify those L which are isomorphic to the Li e algebra aff2 of the group Aff2(K< /i>) of affine transformations of A2. We then show that the following statements are equivalent:
(a) The Jacobian Conjecture holds in dimension 2\;
(b) All Lie subalgebras L ⊂ Vecc (A2) isomorphic to aff2 are conj ugate under Aut(A2)\;
(c) All Lie subalgebras L< /i> ⊂ Vecc(A2) isomorphic to aff2 are algebraic. DTEND;TZID=Europe/Zurich:20131122T120000 END:VEVENT BEGIN:VEVENT UID:news729@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T202615 DTSTART;TZID=Europe/Zurich:20131118T141500 SUMMARY:Seminar Algebra and Geometry: Gerry Schwarz (Brandeis University) DESCRIPTION:Let $\\mathfrak g$ be a simple complex Lie algebra and let G be the corresponding adjoint group. Consider the G-module V which is the d irect sum of r copies of $\\mathfrak g$.  We say that V is \\emph{large\ \/} if r≥2 and r≥3 if G has rank 1. We showed that when V is large an y algebraic automorphism ψ of the quotient Z:=V//G lifts to an algebrai c  mapping Ψ:V→V which sends the fiber over z to the fiber over ψ(z) \, z ∈ Z. (Most cases were already handled by work of Kuttler)We also s howed that one can choose a biholomorphic lift Ψ such that Ψ(gv)=σ(g) Ψ(v)\, g ∈ G\, v ∈ V\, where σ is an automorphism of G. This leaves open  the following questions: Can one lift holomorphic automorphisms o f Z? Which automorphisms lift if  V is not large? We answer  the first question in the affirmative and also answer the second question. X-ALT-DESC: Let $\\mathfrak g$ be a simple complex Lie algebra and let G be the corresponding adjoint group. Consider the G-module V which is the d irect sum of r copies of $\\mathfrak g$. \; We say that V is \\emph{l arge\\/} if r≥2 and r≥3 if G has rank 1. We showed that when V is lar ge any algebraic automorphism \;ψ of the quotient Z:=V//G lifts to a n algebraic \; mapping Ψ:V→V which sends the fiber over z to the f iber over ψ(z)\, z ∈ Z. (Most cases were already handled by work of Ku ttler)
We also showed that one can choose a biholomorphic lift Ψ su ch that Ψ(gv)=σ(g)Ψ(v)\, g ∈ G\, v ∈ V\, where σ is an automorphi sm of G. This leaves open \; the following questions: Can one lift ho lomorphic automorphisms of Z? Which automorphisms lift if \; V is not large? We answer \; the first question in the affirmative and also a nswer the second question. DTEND;TZID=Europe/Zurich:20131118T154500 END:VEVENT BEGIN:VEVENT UID:news730@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T202907 DTSTART;TZID=Europe/Zurich:20131115T103000 SUMMARY:Seminar Algebra and Geometry: Jan Draisma (Universiteit Eindhoven) DESCRIPTION:I will introduce the notion of Plücker variety\, which is a ru le that assigns to a pair of a natural number p and a finite-dimensional vector space V a closed subvariety of the p-th exterior power of V. To be a Plücker variety\, the rule should satisfy two axioms\, one of which i s functoriality in V. The Grassmannian is the smallest nonempty Plücker variety\, and the class of Plücker varieties is closed under joins\, tangential varieties\, unions\, and intersections. I will sketch a proof that any "bounded"  Plücker variety is defined set-theoretically by e quations of bounded degree\, and in fact by finitely many equations up t o symmetry. So far\, this statement was unknown even for the first secan t variety of the Grassmannian. The talk is based on joint work with Rob Eggermont\, and inspired by Snowden's work on Delta-varieties. X-ALT-DESC: I will introduce the notion of Plücker variety\, which is a ru le that assigns to a pair of a natural number p and a finite-dimen sional vector space V a closed subvariety of the p-th exter ior power of V. To be a Plücker variety\, the rule should satisfy two axioms\, one of which is functoriality in V. The Grassmannia n is the smallest nonempty Plücker variety\, and the class of Plücker varieties is closed under joins\, tangential varieties\, unions\, and in tersections.

I will sketch a proof that any "\;bounded&q uot\; \; Plücker variety is defined set-theoretically by equations o f bounded degree\, and in fact by finitely many equations up to symmetry . So far\, this statement was unknown even for the first secant variety of the Grassmannian. The talk is based on joint work with Rob Eggermont \, and inspired by Snowden's work on Delta-varieties. DTEND;TZID=Europe/Zurich:20131115T120000 END:VEVENT BEGIN:VEVENT UID:news731@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T203228 DTSTART;TZID=Europe/Zurich:20131108T103000 SUMMARY:Seminar Algebra and Geometry: Matthias Leuenberger (Universität B ern) DESCRIPTION:For Cn the Lie algebra generated by locally nilpotent derivati ons (LNDs) is equal to the Lie algebra of all divergence free algebraic vector fields. It is not known which other smooth affine varieties have this property. We will see an answer to this question for smooth surfac es given by xy=p(z): It turns out that here the Lie algebra generated by LNDs is a subalgebra of codimension deg(p)-2 inside the divergence free vector fields. X-ALT-DESC: For Cn the Lie algebra generated by locally n ilpotent derivations (LNDs) is equal to the Lie algebra of all divergenc e free algebraic vector fields. It is not known which other smooth affin e varieties have this property. We will see an answer to this question for smooth surfaces given by xy=p(z): It turns out that here the Lie al gebra generated by LNDs is a subalgebra of codimension deg(p)-2 inside t he divergence free vector fields. DTEND;TZID=Europe/Zurich:20131108T120000 END:VEVENT BEGIN:VEVENT UID:news732@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T203628 DTSTART;TZID=Europe/Zurich:20131101T103000 SUMMARY:Seminar Algebra and Geometry: Alberto Calabri (Università di Ferr ara) DESCRIPTION:Fixed a positive integer d\, plane Cremona transformations of d egree d form a quasi-projective variety. Its decomposition in irreducible components\, their dimension and the properties of the general element o f each irreducible component will be presented. Its connectedness will be discussed for small values of d. This is joint work with Cinzia Bisi and Massimiliano Mella. X-ALT-DESC: Fixed a positive integer d\, plane Cremona transformations of d egree d form a quasi-projective variety. Its decomposition in irreducible components\, their dimension and the properties of the general element o f each irreducible component will be presented. Its connectedness will be discussed for small values of d. This is joint work with Cinzia Bisi and Massimiliano Mella. DTEND;TZID=Europe/Zurich:20131101T120000 END:VEVENT BEGIN:VEVENT UID:news733@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T203934 DTSTART;TZID=Europe/Zurich:20131025T103000 SUMMARY:Seminar Algebra and Geometry: Roland Lötscher (Universität Münch en) DESCRIPTION:Essential dimension of fibered categories X-ALT-DESC:Essential dimension of fibered categories DTEND;TZID=Europe/Zurich:20131025T120000 END:VEVENT BEGIN:VEVENT UID:news734@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T204230 DTSTART;TZID=Europe/Zurich:20131018T103000 SUMMARY:Seminar Algebra and Geometry: Pascal Rolli (ETH Zürich) DESCRIPTION:A quasimorphism (QM) is a real-valued function on a group that almost behaves like a homomorphism. Non-trivial QMs exist whenever the gr oup has some features of negative curvature\, for example when it is Grom ov hyperbolic. I will discuss old and new constructions of QMs\, using c ombinatorial\, geometric and algebraic ideas. In a second part I will tal k about the relation to cohomology. To each QM there is an associated cla ss in the group's second bounded cohomology $H^2_b$. One of our QM constr uctions yields linear isometric embeddings so called defect spaces into $ H^2_b$. These spaces have an interesting geometry\, they are l∞ spaces e quipped with an exotic norm. X-ALT-DESC: A quasimorphism (QM) is a real-valued function on a group that almost behaves like a homomorphism. Non-trivial QMs exist whenever the gr oup has some features of negative curvature\, for example when it is Grom ov hyperbolic. I will discuss old and new constructions of QMs\, using c ombinatorial\, geometric and algebraic ideas. In a second part I will tal k about the relation to cohomology. To each QM there is an associated cla ss in the group's second bounded cohomology $H^2_b$. One of our QM constr uctions yields linear isometric embeddings so called defect spaces into $ H^2_b$. These spaces have an interesting geometry\, they are l∞ spaces equipped with an exotic norm. DTEND;TZID=Europe/Zurich:20131018T120000 END:VEVENT BEGIN:VEVENT UID:news735@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T204531 DTSTART;TZID=Europe/Zurich:20131011T103000 SUMMARY:Seminar Algebra and Geometry: Isac Hedén (Universität Basel) DESCRIPTION:We study complex affine Ga-threefolds X with the affine plane A 2 as their algebraic quotient\, and which are a principal bundle over the punctured affine plane A2*. Changing the point of view\, we look for affin e extensions of Ga-principal bundles over A2* that are obtained by adding an extra fiber to the bundle projection over the origin. It turns out that SL2 plays a special role\, since every Ga-principal bundle can be obtaine d as a pullback of SL2. We construct two series of such extensions which g eneralize the basic extension obtained by adding a zero section to SL2 vie wed as a Gm-principal bundle over P1 x P1 \\ Δ. X-ALT-DESC: We study complex affine Ga-threefolds X with the affine plane A2 as their algebraic quotient\, and wh ich are a principal bundle over
the punctured affine plane A< sup>2*. Changing the point of view\, we look for affine e xtensions of Ga-principal bundles over A2* that are obtained by adding an extra fiber to the bundle p rojection over the origin. It turns out that SL2 plays a specia l role\, since every Ga-principal bundle can be obtained as a pullback of SL2. We construct two series of such extensio ns which generalize the basic extension obtained by adding a zero section to SL2 viewed as a Gm-principal bundle over < b>P1 x P1 \\ Δ. DTEND;TZID=Europe/Zurich:20131011T120000 END:VEVENT BEGIN:VEVENT UID:news736@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T211438 DTSTART;TZID=Europe/Zurich:20130531T103000 SUMMARY:Seminar Algebra and Geometry: Adrien Dubouloz (Université de Bourg ogne) DESCRIPTION:A result of Makar-Limanov asserts that if X an affine variety w ithout nontrivial action of the additive group\, then there are no addit ive group actions on the cylinder X x A1 besides the obvious ones by ge neric translations on the second factor. In this talk\, I will give exa mples which illustrate how badly this property can fail for higher dimen sional cylinders. The recipe will involve\, among other ingredients\, ri gid affine cubic surfaces\, some Ga-linearized line bundles and a struct ure theorem for vector bundles over rational affine surfaces\, all mixed together through a variant of the overused Danielewski fiber product tr ick. X-ALT-DESC: A result of Makar-Limanov asserts that if X an affine variety w ithout nontrivial action of the additive group\, then there are no addit ive group actions on the cylinder X x A1 besides the obvious ones by generic translations on the second factor. In this talk\, I wil l give examples which illustrate how badly this property can fail for h igher dimensional cylinders. The recipe will involve\, among other ingre dients\, rigid affine cubic surfaces\, some Ga-linearized lin e bundles and a structure theorem for vector bundles over rational affin e surfaces\, all mixed together through a variant of the overused Daniel ewski fiber product trick. DTEND;TZID=Europe/Zurich:20130531T120000 END:VEVENT BEGIN:VEVENT UID:news737@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T211745 DTSTART;TZID=Europe/Zurich:20130524T103000 SUMMARY:Seminar Algebra and Geometry: Andrea Marinatto (Università di Udin e) DESCRIPTION:Let K be a perfect field of characteristic not equal to two\, $ \\bar{K}$ an algebraic closure of K and let GK be the Galois group of the extension $\\bar{K}/K$.  Let T be a n-point set in $P1(\\bar{K})$. The fi eld of moduli of T is contained in each field of definition but it is not necessarily a field of definition. In this seminar we show that point se ts of odd cardinality n≥5 in  $P1(\\bar{K})$ with field of moduli K a re defined over their field of moduli. We\, also\, show that\, except for the special case of the 4-point sets\, this does not hold in general for point sets of even cardinality n≥6. X-ALT-DESC: Let K be a perfect field of characteristic not equal to two\, $\\bar{K}$ an algebraic closure of K and let GK be the Galois group of the extension $\\bar{K}/K$. \; Let T be a n-point set in $P1(\\bar{K})$. The field of modul i of T is contained in each field of definition but it is not nece ssarily a field of definition. In this seminar we show that point sets of odd cardinality n≥5 in \; $P1(\\bar{K})$ with fi eld of moduli K are defined over their field of moduli. We\, also\ , show that\, except for the special case of the 4-point sets\, this does not hold in general for point sets of even cardinality n≥6. DTEND;TZID=Europe/Zurich:20130524T120000 END:VEVENT BEGIN:VEVENT UID:news738@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T211954 DTSTART;TZID=Europe/Zurich:20130517T103000 SUMMARY:Seminar Algebra and Geometry: Susanna Zimmermann (Universität Bas el) DESCRIPTION:Geometry and Invariants of the Affine Group X-ALT-DESC:Geometry and Invariants of the Affine Group DTEND;TZID=Europe/Zurich:20130517T120000 END:VEVENT BEGIN:VEVENT UID:news739@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T212734 DTSTART;TZID=Europe/Zurich:20130503T103000 SUMMARY:Seminar Algebra and Geometry: Sergei Kovalenko (Ruhr-Universität B ochum) DESCRIPTION:Gizatullin surfaces are normal affine surfaces completable by a zigzag\, i. e. by a linear chain of smooth rational curves. An equivalen t characterization of such surfaces V\, except for the surface C∗ × C ∗\, is that the automorphism group acts with a big orbit O\, i. e. V \\ O is finite. Considering some examples of Gizatullin surfaces like the aff ine plane A2 or the Danielewski surfaces V = {xy − P(z) = 0} ⊆ A3 it f ollows that the big orbit O coincides with the smooth locus Vreg . Gizatul lin formulated in his pioneer works the following conjecture: \\r\\nConjec ture (Gizatullin): The big orbit of a Gizatullin surface V coincides with its smooth locus\, i. e. O = Vreg . \\r\\nWe show that the action of the a utomorphism group of a smooth Gizatullin surface with a distinguished and rigid extended divisor is not transitive in general. Thus such surfaces represent counterexamples to Gizatullin’s conjecture. For such surfaces we give an explicit orbit decomposition of the natural action of the aut omorphism group. Moreover\, the automorphism group of such smooth Gizatul lin surfaces can be represented as an amalgamated product of two automorp hism subgroups. X-ALT-DESC:Gizatullin surfaces are normal affine surfaces completable by a zigzag\, i. e. by a linear chain of smooth rational curves. An equivalent characterization of such surfaces V\, except for the surface C ∗ × C∗\, is that the automorphism gr oup acts with a big orbit O\, i. e. V \\ O is finite. Considering some examples of Gizatullin surfaces like the affine plane A2 or the Danielewski surfaces V = {xy − P(z) = 0} ⊆ < b>A3 it follows that the big orbit O coincides with the smooth locus Vreg . Gizatullin formulated in his pio neer works the following conjecture: \nConjecture (Gizatullin): The big orbit of a Gizatullin surface V coincides with its smooth locu s\, i. e. O = Vreg . \nWe show that the action of the au tomorphism group of a smooth Gizatullin surface with a distinguished and rigid extended divisor is not transitive in general. Thus such surfaces r epresent counterexamples to Gizatullin’s conjecture. For such surfaces we give an explicit orbit decomposition of the natural action of the auto morphism group. Moreover\, the automorphism group of such smooth Gizatull in surfaces can be represented as an amalgamated product of two automorph ism subgroups. DTEND;TZID=Europe/Zurich:20130503T120000 END:VEVENT BEGIN:VEVENT UID:news740@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T213008 DTSTART;TZID=Europe/Zurich:20130426T103000 SUMMARY:Seminar Algebra and Geometry: Arnaud Beauville (Université de Nice ) DESCRIPTION:The Lüroth problem asks whether every field K with C ⊂ K ⊂ C(x1\,...\,xn) is of the form C(y1\,...\,yp). In geometric terms\, if an algebraic variety can be parametrized by rational functions\, can one f ind a one-to-one such parametrization? After a brief historical survey\, I will recall the counter-examples found in the 70's\; then I will desc ribe a quite simple (and new) counter-example\, and its application to t he study of finite simple groups of birational automorphisms of P3. X-ALT-DESC: The Lüroth problem asks whether every field K with C ⊂ K ⊂ C(x1\,...\,xn) is of th e form C(y1\,...\,yp). In geometric terms\, if an algebraic variety can be parametrized by rational functions\, can one find a one-to-one such parametrization?
After a brief historic al survey\, I will recall the counter-examples found in the 70's\; then I will describe a quite simple (and new) counter-example\, and its appli cation to the study of finite simple groups of birational automorphisms of P3. DTEND;TZID=Europe/Zurich:20130426T120000 END:VEVENT BEGIN:VEVENT UID:news741@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T213334 DTSTART;TZID=Europe/Zurich:20130419T103000 SUMMARY:Seminar Algebra and Geometry: Jan Draisma (Technische Universiteit Eindhoven) DESCRIPTION:The maximum-likelihood degree of a smooth\, locally closed subv ariety X of a torus (C*)n is the number of critical points on X of any mon omial function    (p1\,...\,pn) --> p1u1... pnunwith u in Nn sufficient ly general. This notion is motivated by statistics\, where X is a family o f probability distributions on {1\,...\,n}\, u records observed data\, and the maximum-likelihood estimate for p given u is one of the critical poin ts of the function above.In recent work by Hauenstein\, Rodriguez\, and S turmfels the maximum-likelihood degree of determinantal varieties was stu died. Extensive computations using numerical algebraic geometry led to th e conjecture that the maximum-likelihood degree of the variety of rank-r matrices whose entries add up to 1 equals that of the variety of corank- (r-1) matrices whose entries add up to 1. I will present a proof of that conjecture\, and variations of it for symmetric and skew-symmetric matric es.  Joint work with Jose Rodriguez. X-ALT-DESC: The maximum-likelihood degree of a smooth\, locally closed subv ariety X of a torus (C*)n is the number of critic al points on X of any monomial function
 \; \; \; (p1\,...\,pn) -->\; p1u1... pnun
with u in Nn sufficiently g eneral. This notion is motivated by statistics\, where X is a famil y of probability distributions on {1\,...\,n}\, u records observed data\, and the maximum-likelihood estimate for p given u is one of the critical points of the function above.

In recent wo rk by Hauenstein\, Rodriguez\, and Sturmfels the maximum-likelihood degre e of determinantal varieties was studied. Extensive computations using nu merical algebraic geometry led to the conjecture that the maximum-likelih ood degree of the variety of rank-r matrices whose entries add up to 1 eq uals that of the variety of corank-(r-1) matrices whose entries add up to 1. I will present a proof of that conjecture\, and variations of it for symmetric and skew-symmetric matrices. \; Joint work with Jose Rodrig uez. DTEND;TZID=Europe/Zurich:20130419T120000 END:VEVENT BEGIN:VEVENT UID:news742@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T221148 DTSTART;TZID=Europe/Zurich:20130412T103000 SUMMARY:Seminar Algebra and Geometry: Antoine Ducros (Université Paris 6) DESCRIPTION:If one tries to mimic naively in the  p-adic setting what is u sually done in complex analytic geometry\, one immediately faces big probl ems\, because p-adic fields are totally disconnected. Hence in order to de velop a relevant p-adic geometry\, a more subtle approach is needed. In this talk\, I will begin with a presentation of that of Berkovich. It r oughly consists of 'adding plenty of points' to the usual p-adic spaces s o that they get good topological properties (like local path-connectedne ss). I will describe some Berkovich spaces associated with simple variet ies (the projective line\, the algebraic curves....). \\r\\nThen I will try to illustrate the following slogan: 'to see the good analog of a comp lex object in the p-adic world\, one often has to work with Berkovich spa ces'\, through three examples: spectral theory\; dynamical systems\; and the theory of real (p\,q)-forms and related notions (integrals\, bounda ry integrals\, curvature forms of metrized line bundles) that as been r ecently developped in the framework of Berkovich spaces by Chambert-Loir and myself\, and that I will try to describe in some detail. X-ALT-DESC:If one tries to mimic naively in the \; p-adic settin g what is usually done in complex analytic geometry\, one immediately face s big problems\, because p-adic fields are totally disconnected. He nce in order to develop a relevant p-adic geometry\, a more subtle approach is needed.

In this talk\, I will begin with a pres entation of that of Berkovich. It roughly consists of 'adding plenty of points' to the usual p-adic spaces so that they get good topologic al properties (like local path-connectedness). I will describe some Berk ovich spaces associated with simple varieties (the projective line\, the algebraic curves....).
\nThen I will try to illustrate the follo wing slogan: 'to see the good analog of a complex object in the p-a dic world\, one often has to work with Berkovich spaces'\, through three examples: spectral theory\; dynamical systems\; and the theory of real (p\,q)-forms and related notions (integrals\, boundary integrals\, curv ature forms of metrized line bundles) that as been recently developped i n the framework of Berkovich spaces by Chambert-Loir and myself\, and th at I will try to describe in some detail. DTEND;TZID=Europe/Zurich:20130412T120000 END:VEVENT BEGIN:VEVENT UID:news743@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T221406 DTSTART;TZID=Europe/Zurich:20130405T103000 SUMMARY:Seminar Algebra and Geometry: Alexander Perepechko (Moscow State Un iversity and Institut Fourier\, Grenoble) DESCRIPTION:Infinite transitivity on universal torsors X-ALT-DESC:Infinite transitivity on universal torsors DTEND;TZID=Europe/Zurich:20130405T120000 END:VEVENT BEGIN:VEVENT UID:news744@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T221955 DTSTART;TZID=Europe/Zurich:20130315T103000 SUMMARY:Seminar Algebra and Geometry: Christian Urech (Universität Basel) DESCRIPTION:The affine Cremona group $\\mathcal{G}_n$ is the group of polyn omial automorphisms of An. Hanspeter Kraft and Immanuel Stampfli showed that every automorphism of $\\mathcal{G}_n$ as a group is inner up to f ield automorphism if restricted to the subgroup of tame automorphisms. F irst I will sketch a proof of this theorem. \\r\\n In a next step we onl y consider those automorphisms of $\\mathcal{G}_n$ that also respect its additional algebraic structure as an ind-group. It turns out that these are exactly the inner automorphisms of $\\mathcal{G}_n$. To prove this I will follow an idea recently presented by Belov-Kanel and Yu\, which u ses tame approximation. \\r\\nThese are results from my Master's thesis under the supervision of Hanspeter Kraft. X-ALT-DESC:The affine Cremona group $\\mathcal{G}_n$ is the group of polyno mial automorphisms of An. Hanspeter Kraft and Immanuel Stampfli showed that every automorphism of $\\mathcal{G}_n$ as a group is inner up to field automorphism if restricted to the subgroup of tame automorphisms. First I will sketch a proof of this theorem. \n In a nex t step we only consider those automorphisms of $\\mathcal{G}_n$ that als o respect its additional algebraic structure as an ind-group. It turns o ut that these are exactly the inner automorphisms of $\\mathcal{G}_n$. T o prove this I will follow an idea recently presented by Belov-Kanel and Yu\, which uses tame approximation. \nThese are results from my Master' s thesis under the supervision of Hanspeter Kraft. DTEND;TZID=Europe/Zurich:20130315T120000 END:VEVENT BEGIN:VEVENT UID:news745@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T223128 DTSTART;TZID=Europe/Zurich:20130308T103000 SUMMARY:Seminar Algebra and Geometry: Vladimir Bavula (University of Sheffi eld) DESCRIPTION:An analogue of the Conjecture of Dixmier is true for the algebr a of polynomial integro-differential operators \\r\\nIn 1968\, Dixmier pos ed six problems for the algebra of polynomial differential operators\, i. e. the Weyl algebra. In 1975\, Joseph solved the third and sixth problems and\, in 2005\, I solved the fifth problem and gave a positive solution to the fourth problem but only for homogeneous differential operators. Th e remaining three problems are still open. The first problem/conjecture o f Dixmier (which is equivalent to the Jacobian Conjecture as was shown in 2005-07 by Tsuchimito\, Belov and Kontsevich) claims that the Weyl algeb ra 'behaves' as a  finite field extension. In more detail\, the first pr oblem/conjecture of Dixmier asks: is it true that an algebra endomorphism of the Weyl algebra is an automorphism? In 2010\, I proved that this que stion has an affirmative answer for the algebra of polynomial integro-dif ferential operators. In my talk\, I will explain  the main ideas\, the s tructure of the proof and recent progress on the first problem/conjecture of Dixmier. \\r\\nThe group of automorphisms of the  algebra of one-side d inverses of a polynomial algebra \\r\\nThe algebra Sn of one-sided inver ses of a polynomial algebra Pn in n variables is obtained from Pn by addi ng commuting\, left (but not two-sided) inverses of its canonical generat ors. Ignoring non-Noetherian property\, the algebra Sn belongs to a family of algebras like the n'th Weyl algebra  and the polynomial algebra in 2n variables (e.g.\, the Gelfand-Kirillov dimension of Sn is 2n).The group o f automorphisms Gn of Sn is huge. Recently\, I found the group Gn and its explicit generators. In my talk\,  I will explain the ideas behind the proofs and I will do an overview of the basic properties of these algebra s and their connections with polynomials\, differential and integro-diffe rential operators. X-ALT-DESC:An analogue of the Conjecture of Dixmier is true for the alge bra of polynomial integro-differential operators \nIn 19 68\, Dixmier posed six problems for the algebra of polynomial differentia l operators\, i.e. the Weyl algebra. In 1975\, Joseph solved the third an d sixth problems and\, in 2005\, I solved the fifth problem and gave a po sitive solution to the fourth problem but only for homogeneous differenti al operators. The remaining three problems are still open. The first prob lem/conjecture of Dixmier (which is equivalent to the Jacobian Conjecture as was shown in 2005-07 by Tsuchimito\, Belov and Kontsevich) claims tha t the Weyl algebra 'behaves' as a \; finite field extension. In more detail\, the first problem/conjecture of Dixmier asks: is it true that an algebra endomorphism of the Weyl algebra is an automorphism? In 2010\, I proved that this question has an affirmative answer for the algebra of p olynomial integro-differential operators. In my talk\, I will explain&nbs p\; the main ideas\, the structure of the proof and recent progress on th e first problem/conjecture of Dixmier. \nThe group of automorphisms of the \; algebra of one-sided inverses of a polynomial alg ebra \nThe algebra Sn of one-sided inverses o f a polynomial algebra Pn in n variables is obtai ned from Pn by adding commuting\, left (but not two-sid ed) inverses of its canonical generators. Ignoring non-Noetherian propert y\, the algebra Sn belongs to a family of algebras like the n'th Weyl algebra \; and the polynomial algebra in 2n variables (e.g.\, the Gelfand-Kirillov dimension of Sn is 2n).
The group of automorphisms Gn of Snis huge. Recently\, I found the group Gn< /i> and its explicit generators. In my talk\, \; I will explain the i deas behind the proofs and I will do an overview of the basic properties of these algebras and their connections with polynomials\, differential a nd integro-differential operators. DTEND;TZID=Europe/Zurich:20130308T120000 END:VEVENT BEGIN:VEVENT UID:news746@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T223007 DTSTART;TZID=Europe/Zurich:20130301T103000 SUMMARY:Seminar Algebra and Geometry: Jérémy Blanc (Universität Basel) DESCRIPTION:A classical theorem says that del Pezzo surfaces are\, with the exception of the smooth quadric\, blow-ups of the plane into at most 8 points\, such that no three are collinear\, no 6 on the same conic and n o 8 on the same cubic\, singular at one of the 8 points. Moreover\, a general set of at most 8 points of the plane satisfies these conditions. \\r\\nI will describe the theorem\, give the proof\, and describe the g eneralisation to dimension 3\, by considering blow-ups of points and cur ves in the projective space. We can get similar descriptions\, the condi tions of generality are now in terms of multisecant lines\, conic or twi sted cubics.\\r\\nJoint work with Stéphane Lamy. X-ALT-DESC:A classical theorem says that del Pezzo surfaces are\, with the exception of the smooth quadric\, blow-ups of the plane into at most 8 points\, such that no three are collinear\, no 6 on the same conic and no 8 on the same cubic\, singular at one of the 8 points. Moreover\, a g eneral set of at most 8 points of the plane satisfies these conditions. \nI will describe the theorem\, give the proof\, and describe the genera lisation to dimension 3\, by considering blow-ups of points and curves i n the projective space. We can get similar descriptions\, the conditions of generality are now in terms of multisecant lines\, conic or twisted cubics.\nJoint work with Stéphane Lamy. DTEND;TZID=Europe/Zurich:20130301T120000 END:VEVENT BEGIN:VEVENT UID:news747@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T231411 DTSTART;TZID=Europe/Zurich:20121214T103000 SUMMARY:Seminar Algebra and Geometry: Ronan Terpereau (Université Joseph F ourier\, Grenoble) DESCRIPTION:Let G be a classical group (SL(V)\, GL(V)\, O(V)\,...) and X be the direct sum of p copies of the standard representation of G and q copi es of its dual representation\, where p and q are positive integers. We co nsider the invariant Hilbert scheme\, denoted H\, which parametrizes the G -stable closed subschemes Z of X such that k[Z] is isomorphic to the regul ar representation of G.   \\r\\n    In this talk\, we will see that H is a smooth variety when the dimension of V is small\, but that H is gener ally singular. When H is smooth\, the Hilbert-Chow morphism H -> X//G is a canonical resolution of the singularities of the categorical quotient X// G (=Spec(k[X]G)). Then it is natural to ask what are the good geometric pr operties of this resolution (for instance if it is crepant). \\r\\n    T o finish\, we will mention some analogue results in the symplectic setting \, that is to say by letting p=q and replacing X by the zero fiber of the moment map. The quotients that we get by doing this are isomorphic to th e closures of nilpotent orbits\, and the Hilbert-Chow morphism is a resol ution of their singularities (sometimes a symplectic one). X-ALT-DESC:Let G be a classical group (SL(V)\, GL(V)\, O(V)\,...) and X be the direct sum of p copies of the standard representation of G and q copie s of its dual representation\, where p and q are positive integers. We con sider the invariant Hilbert scheme\, denoted H\, which parametrizes the G- stable closed subschemes Z of X such that k[Z] is isomorphic to the regula r representation of G. \;  \;\n \;  \; In this talk\, we w ill see that H is a smooth variety when the dimension of V i s small\, but that H is generally singular. When H is smooth \, the Hilbert-Chow morphism H ->\; X//G is a canon ical resolution of the singularities of the categorical quotient X/ /G (=Spec(k[X]G)). Then it is natur al to ask what are the good geometric properties of this resolution (for i nstance if it is crepant). \n \;  \; To finish\, we will mention s ome analogue results in the symplectic setting\, that is to say by letting p=q and replacing X by the zero fiber of the moment map. The quotients that we get by doing this are isomorphic to the closu res of nilpotent orbits\, and the Hilbert-Chow morphism is a resolution o f their singularities (sometimes a symplectic one). DTEND;TZID=Europe/Zurich:20121214T120000 END:VEVENT BEGIN:VEVENT UID:news748@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T231746 DTSTART;TZID=Europe/Zurich:20121207T103000 SUMMARY:Seminar Algebra and Geometry: Matthieu Jacquemet (Université de Fr ibourg) DESCRIPTION:We are interested in estimating the volume of a hyperbolic n-po lyhedron by knowing its f-vector\, and its 'inradius'. In fact\, exact v olume formulas are difficult to find for n>2. However\, in dimension 3\, there is a volume estimate by Fejes-Toth (for spaces of constant curvat ure) in terms of the inradius and the f-vector\, showing some deficienci es. A natural question in this context (but also in general) is the inradi us of a hyperbolic simplex. I shall start with a (partial) overview of t he context of hyperbolic orbifolds/manifolds and their volume. In a seco nd part\, I shall discuss Fejes-Toth's result and give some new results for compact simplices in any dimensions. X-ALT-DESC: We are interested in estimating the volume of a hyperbolic n-po lyhedron by knowing its f-vector\, and its 'inradius'. In fact\, exact v olume formulas are difficult to find for n>\;2. However\, in dimension 3\, there is a volume estimate by Fejes-Toth (for spaces of constant cu rvature) in terms of the inradius and the f-vector\, showing some defici encies. A natural question in this context (but also in general) is the in radius of a hyperbolic simplex. I shall start with a (partial) overview of the context of hyperbolic orbifolds/manifolds and their volume. In a second part\, I shall discuss Fejes-Toth's result and give some new resu lts for compact simplices in any dimensions. DTEND;TZID=Europe/Zurich:20121207T120000 END:VEVENT BEGIN:VEVENT UID:news749@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T232040 DTSTART;TZID=Europe/Zurich:20121123T103000 SUMMARY:Seminar Algebra and Geometry: Jung Kyu Canci (Universität Basel) DESCRIPTION:We will see some results in diophantine geometry and the ir applications to some problems in arithmetic of dynamical systems.  These problems are related to the Morton and Silverman's Uniform B oundedness Conjecture on preperiodic points for rational maps. X-ALT-DESC: We \;will \;see \;some \;results in \;dioph antine \;geometry and \;their applications to \;some \;pr oblems in \;arithmetic of \;dynamical systems. \;These \;p roblems are \;related to the Morton and \;Silverman's Uniform&nb sp\;Boundedness Conjecture on \;preperiodic points for rational maps. DTEND;TZID=Europe/Zurich:20121123T120000 END:VEVENT BEGIN:VEVENT UID:news750@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T232355 DTSTART;TZID=Europe/Zurich:20121109T103000 SUMMARY:Seminar Algebra and Geometry: Yves de Cornulier (Laboratoire de Mat hématiques d'Orsay) DESCRIPTION:I will give "algebraic presentations" of algebraic groups\, and develop\, as consequences: Abels' criterion for a p-adic algebraic grou p to be compactly presented\, and polynomial estimates on the Dehn functi on of real or p-adic algebraic groups. X-ALT-DESC: I will give "\;algebraic presentations"\; of algebraic groups\, and develop\, as consequences: Abels' criterion for a p-a dic algebraic group to be compactly presented\, and polynomial estimates on the Dehn function of real or p-adic algebraic groups. DTEND;TZID=Europe/Zurich:20121109T120000 END:VEVENT BEGIN:VEVENT UID:news751@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190211T235825 DTSTART;TZID=Europe/Zurich:20121026T103000 SUMMARY:Seminar Algebra and Geometry: Émilie Dufresne (Universität Basel) DESCRIPTION:The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Ra ther than considering the whole ring of invariants\, one considers a sep arating set\, that is\, a set of invariants whose elements separate any t wo points which can be separated by invariants. One of the appeals of thi s new approach is that separating invariants can have better structural a nd computational properties than the ring of invariants. For example\, th ere always exist a finite separating set\, no matter the group. In this t alk\, we study well-behaved separating algebras for invariants of represe ntations of finite groups. In particular\, we show that if there exists a polynomial separating algebra\, the the group action must be generated b y (pseudo-)reflections. X-ALT-DESC: The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Ra ther than considering the whole ring of invariants\, one considers a sep arating set\, that is\, a set of invariants whose elements separate any t wo points which can be separated by invariants. One of the appeals of thi s new approach is that separating invariants can have better structural a nd computational properties than the ring of invariants. For example\, th ere always exist a finite separating set\, no matter the group. In this t alk\, we study well-behaved separating algebras for invariants of represe ntations of finite groups. In particular\, we show that if there exists a polynomial separating algebra\, the the group action must be generated b y (pseudo-)reflections. DTEND;TZID=Europe/Zurich:20121026T120000 END:VEVENT BEGIN:VEVENT UID:news752@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T000335 DTSTART;TZID=Europe/Zurich:20121012T103000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Universität Basel) DESCRIPTION:Let X\,Y be two complex varieties and assume that there is an (abstract) isomorphism of the semigroups End(X) and End(Y). If one of the varieties is affine and contains a copy of the affine line\, then X and Y are isomorphic\, up to a field automorphism. I will explain the proof of this amazing result which is base on an old theorem due to Dick Palai s. X-ALT-DESC: Let X\,Y be two complex varieties and assume that there is an (abstract) isomorphism of the semigroups End(X) and E nd(Y). If one of the varieties is affine and contains a copy of th e affine line\, then X and Y are isomorphic\, up to a fiel d automorphism. I will explain the proof of this amazing result which is base on an old theorem due to Dick Palais. DTEND;TZID=Europe/Zurich:20121012T120000 END:VEVENT BEGIN:VEVENT UID:news753@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T001023 DTSTART;TZID=Europe/Zurich:20121005T103000 SUMMARY:Seminar Algebra and Geometry: Matteo Ruggiero (École polytechnique ) DESCRIPTION:In the last years valuative theory has been used (see the work s of Favre\, Jonsson\, Boucksom\, and others) to study several dynamic al properties in both local and global settings. I shall present a join t work with William Gignac\, on the growth of attracting rates for itera tes of a superattracting germ in C2. If time allows\, I will present other applications and examples. X-ALT-DESC: In the last years valuative theory has been used \;(see the works of Favre\, Jonsson\, Boucksom\, \;and others) \;to study several dynamical properties in both local and global settings.
I shall present a joint work with William Gignac\, on the growth of attrac ting rates for iterates of a superattracting germ in C2.
If time allows\, I will present other applications and examples. DTEND;TZID=Europe/Zurich:20121005T120000 END:VEVENT BEGIN:VEVENT UID:news754@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T001338 DTSTART;TZID=Europe/Zurich:20120601T103000 SUMMARY:Seminar Algebra and Geometry: Danny de Jesus Gomez (Universität Os nabrück) DESCRIPTION:Let R be a commutative ring with unity\; f\,f1\,...\,fn elemen ts of R (data) and I=(f1\,...\,fn)\, the corresponding ideal of R. The F orcing Algebra A:=R[T1\,...\,Tn]/(f1T1+...+fnTn-f) for the data f\,f1\,.. .\,fn is the most "natural" R-algebra such that f belongs to the expansio n of I in A. On this talk we present criteria and properties over the ba se ring R and the data in order to guarantee the connectedness of the cor responding forcing scheme Spec A. In particular\, we present an arithme tical Criteria for Principal Ideals Domains. Besides\, we rewrite the con dition of belonging to the integral closure of I by means of the univers al connectedness of the canonical morphism between the forcing scheme and the base space Spec R. Finally\, we study the local nature (over the bas e) of the connectedness in a very general setting. X-ALT-DESC:Let R be a commutative ring with unity\; f\,f< /i>1\,...\,fn elements of R (data) and I=(f1\,...\,fn)\, the corresp onding ideal of R. The Forcing Algebra \;A:=R[T1\,...\,Tn]/(f1T1+...+fnTn-f) for the data f\,f1\,...\,fn is the most "\;natural"\; R-algebra such that f belongs to the expansion of I in \;A. On this talk we present crit eria and properties over the base ring R and the data in order to guarantee the connectedness of the corresponding forcing scheme \;Spe c A. In particular\, we present an arithmetical Criteria for Prin cipal Ideals Domains. Besides\, we rewrite the condition of belonging to the integral closure of I by means of the universal connectedness of the canonical morphism between the forcing scheme and the base space Spec R. Finally\, we study the local nature (over the base) of the connectedness in a very general setting. DTEND;TZID=Europe/Zurich:20120601T120000 END:VEVENT BEGIN:VEVENT UID:news755@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T002538 DTSTART;TZID=Europe/Zurich:20120525T103000 SUMMARY:Seminar Algebra and Geometry: Milena Hering (University of Connecti cut) DESCRIPTION:The action of the two-dimensional torus on the plane extends t o an action of the torus on the Hilbert scheme of points in the plane. Th e T-graph is the graph whose vertices are the fixed points under the tor us action (corresponding to monomial ideals)\, where two such vertices ar e connected by an edge if there exists a one-dimensional torus orbit whos e closure contains the corresponding fixed points. I will describe some c onditions for the existence of an edge between two given vertices. \\r\\n This is joint work with Diane Maclaga. X-ALT-DESC:The action of the two-dimensional torus on the plane extends
to an action of the torus on the Hilbert scheme of points in the plane .
The T-graph is the graph whose vertices are the fixed points unde r the
torus action (corresponding to monomial ideals)\, where two such vertices are connected by an edge if there exists a one-dimensional torus orbit whose closure contains the corresponding fixed points. I wil l describe some conditions for the existence of an edge between two given vertices. \nThis is joint work with Diane Maclaga. DTEND;TZID=Europe/Zurich:20120525T120000 END:VEVENT BEGIN:VEVENT UID:news756@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T002832 DTSTART;TZID=Europe/Zurich:20120518T103000 SUMMARY:Seminar Algebra and Geometry: Vladimir Tsygankov\, Gutenberg Univer sität\, Mainz) DESCRIPTION:I will survey briefly known results about  the finite subgroup s in the plane Cremona group over field of complex numbers. The emphasis will be done on the so called ''geometrical method''. By the method the study of the finite subgroups is reduced to  study of so called the ''mi nimal'' finite subgroups of automorphism groups of nonsingular del Pezzo s urfaces and conic bundles. \\r\\nThe description by equations of nonsingu lar Del Pezzo surfaces in weighted projective spaces and description of t heir automorphism groups is a very old completed problem. The description of the ''minimal'' finite subgroups of automorphism groups of nonsingula r del Pezzo surfaces was done by I.V. Dolgachev and V.A. Iskovskikh in 20 07. I constructed a method that allows us to describe  by equations in weighted projective spaces the nonsingular conic bundles with an action o f ''minimal'' subgroup of automorphisms . I applied the method in case\, when the ''minimal'' subgroup of automorphisms is nonsolvable. X-ALT-DESC:I will survey briefly known results about  \;the finite subg roups in the plane Cremona group over field of complex numbers. The empha sis will be done on the so called ''geometrical method''. By the method t he study of the finite subgroups is reduced to  \;study of so called the ''minimal'' finite subgroups of automorphism groups of
nonsingu lar del Pezzo surfaces and conic bundles. \nThe description by equations of nonsingular Del Pezzo surfaces in weighted projective spaces and descr iption of their automorphism groups is a very old completed problem. The description of the ''minimal'' finite subgroups of automorphism groups of nonsingular del Pezzo surfaces was done by I.V. Dolgachev and V.A. Iskov skikh in 2007. I constructed a method that allows us to describe  \;b y equations in weighted projective spaces the nonsingular conic bundles w ith an action of ''minimal'' subgroup of automorphisms . I applied the me thod in case\, when the ''minimal'' subgroup of automorphisms is nonsolva ble. DTEND;TZID=Europe/Zurich:20120518T120000 END:VEVENT BEGIN:VEVENT UID:news757@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T003452 DTSTART;TZID=Europe/Zurich:20120511T103000 SUMMARY:Seminar Algebra and Geometry: Rosa M. Miró-Roig (Universitat de Ba rcelona) DESCRIPTION:In my talk\, I will construct families of non-isomorphic Arithm etically Cohen Macaulay (ACM) sheaves (i.e.\, sheaves without intermediat e cohomology) on projective varieties. Since the seminal result by Horro cks characterizing ACM bundles on $\\mathbb{P}^n$ as those that split int o a sum of line bundles\, an important amount of research has been devote d to the study of ACM sheaves on a given variety.  ACM sheaves also prov ide a criterium to determine the complexity of the underlying variety. Mo re concretely\, this complexity can be studied in terms of the dimension and number of families of indecomposable ACM sheaves that it supports\, n amely its \\emph{representation type}. Along this line\, a variety that a dmits only a finite number of indecomposable ACM sheaves (up to twist and isomorphism) is called of finite representation type. These varieties ar e completely classified: They are either three or less reduced points in $\\mathbb{P}^2$\, a projective space $\\mathbb{P}_k^n$\, a smooth quadric hypersurface $X\\subset\\mathbb{P}^n$\, a cubic scroll in $\\mathbb{P}_k ^4$\, the Veronese surface in $\\mathbb{P}_k^5$ or a rational normal curv e.  On the other extreme of complexity\, we would find the varieties of wild representation type\, namely\, varieties for which there exist r-dime nsional families of non-isomorphic indecomposable ACM sheaves for arbitra ry large r. In the case of dimension one\, it is known that curves of wil d representation type are exactly those of genus larger or equal than two . In dimension greater or equal than two few examples are known ans in ma y talk\, I will give a brief account of the known results. X-ALT-DESC: In my talk\, I will construct families of non-isomorphic Arithm etically Cohen Macaulay (ACM) sheaves (i.e.\, sheaves without intermediat e cohomology) on projective varieties. Since the seminal result by Horro cks characterizing ACM bundles on $\\mathbb{P}^n$ as those that split int o a sum of line bundles\, an important amount of research has been devote d to the study of ACM sheaves on a given variety.
 \;
ACM sheaves also provide a criterium to determine the complexity of the under lying variety. More concretely\, this complexity can be studied in terms of the dimension and number of families of indecomposable ACM sheaves tha t it supports\, namely its \\emph{representation type}. Along this line\, a variety that admits only a finite number of indecomposable ACM sheaves (up to twist and isomorphism) is called of finite representation type . These varieties are completely classified: They are either three or less reduced points in $\\mathbb{P}^2$\, a projective space $\\mathbb{P} _k^n$\, a smooth quadric hypersurface $X\\subset\\mathbb{P}^n$\, a cubic scroll in $\\mathbb{P}_k^4$\, the Veronese surface in $\\mathbb{P}_k^5$ o r a rational normal curve.
 \;
On the other extreme of com plexity\, we would find the varieties of wild representation type\, namely\, varieties for which there exist r-dimensional families of non-is omorphic indecomposable ACM sheaves for arbitrary large r. In the case of dimension one\, it is known that curves of wild representation type are exactly those of genus larger or equal than two. In dimension greater or equal than two few examples are known ans in may talk\, I will give a bri ef account of the known results. DTEND;TZID=Europe/Zurich:20120511T120000 END:VEVENT BEGIN:VEVENT UID:news758@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T003732 DTSTART;TZID=Europe/Zurich:20120504T103000 SUMMARY:Seminar Algebra and Geometry: Clemens Berger (Université de Nice) DESCRIPTION:The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite\, the sum diverges. Nevertheless\, this infinite sum can sometimes be evaluated using generating power series. We show that this is in particular the case when the complex is the simplicial nerve o f a finite category. We discuss the relationship with Rota's notion of Mo ebius inversion and Noguchi's notion of zeta-function of a finite categor y.This talk is based on joint work with Tom Leinster (Glasgow). X-ALT-DESC: The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite\, the sum diverges. Nevertheless\, this infinite sum can sometimes be evaluated using generating power series. We show that this is in particular the case when the complex is the simplicial nerve o f a finite category. We discuss the relationship with Rota's notion of Mo ebius inversion and Noguchi's notion of zeta-function of a finite categor y.

This talk is based on joint work with Tom Leinster (Glasgow) . DTEND;TZID=Europe/Zurich:20120504T120000 END:VEVENT BEGIN:VEVENT UID:news759@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T003913 DTSTART;TZID=Europe/Zurich:20120420T103000 SUMMARY:Seminar Algebra and Geometry: Tommy Wuxing Cai (Universität Basel) DESCRIPTION:We give a formula generalizing Newton's formula on symmetric fu nctions. As an application of it\, we give a simple proof of the existenc e of Macdonald symmetric functions and compute the Macdonald functions of shapes of two-row partitions. X-ALT-DESC: We give a formula generalizing Newton's formula on symmetric fu nctions. As an application of it\, we give a simple proof of the existenc e of Macdonald symmetric functions and compute the Macdonald functions of shapes of two-row partitions. DTEND;TZID=Europe/Zurich:20120420T120000 END:VEVENT BEGIN:VEVENT UID:news760@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T004214 DTSTART;TZID=Europe/Zurich:20120413T103000 SUMMARY:Seminar Algebra and Geometry: Kevin Langlois (Institut Fourier\, Gr enoble) DESCRIPTION:Let A=C[f1\,...\, fr] be an integral algebra of finite type ove r the field of complex numbers.  Using the elements f1\,..\,fr it is diff icult in general to  describe the normalization of A. In this talk\, we p rovide some examples whenever A is a multigraded algebra. Consider the gro up  T=C*×...×C*=(C*)n given by the componentwise multiplication. We say that T is an algebraic torus of dimension n. Let M be the character latti ce of T. Then a T-action on X=Spec A is equivalent to endow A with a M-gra duation. We classify the M-graded algebras A by a number called complexity .  Geometrically\, it corresponds to the codimension of general T-orbits   in X. Algebraically\, the complexity is somehow "the thickness of  gra ded pieces" of the algebra A. The problem of normalization for complexity zero case is well known (monomial or toric case).  For the complexity o ne\, the  normalization of A admits a construction due  to Timashev and Altmann-Hausen in terms of polyhedral divisors over an algebraic  smoot h curve. Taking homogeneous generators\,  we will explain how to build t he polyhedral divisor corresponding  to the normalization of A.  Assume that A is normal. Then A is given by  a polyhedral divisor. A similar p roblem arises for the integral  closure of homogeneous ideals. We will g ive an answer for the complexity one case. We will provide also a classifi cation of homogeneous integrally  closed ideals of A. X-ALT-DESC: Let A=C[f1\,...\, fr] be an integral algebra of finite type over the field of complex numbers. \; Using the elements f1\,..\,fr it is difficult in ge neral to \; describe the normalization of A.

In thi s talk\, we provide some examples whenever A is a multigraded algeb ra.

Consider the group \; T=C*×. ..×C*=(C*)n given by the c omponentwise multiplication. We say that T is an algebraic torus of dimension n. Let M be the character lattice of T. Then a T-action on X=Spec A is equivalent to endow A wi th a M-graduation.

We classify theM-grad ed algebras A by a number called complexity. \; Geometrically\, it corresponds to the codimension of general T-orbits \; in X. Algebraically\, the complexity is somehow "\;the thickness of& nbsp\; graded pieces"\; of the algebra A.

The prob lem of normalization for complexity zero case is well known (monomial or toric case). \; For the complexity one\, the \; normalization of < i>A admits a construction due \; to Timashev and Altmann-Hausen i n terms of polyhedral divisors over an algebraic \; smooth curve. Tak ing homogeneous generators\, \; we will explain how to build the poly hedral divisor corresponding \; to the normalization of A.&nbs p\;

Assume that A is normal. Then A is given by  \; a polyhedral divisor. A similar problem arises for the integral&n bsp\; closure of homogeneous ideals. We will give an answer for the comple xity one case. We will provide also a classification of homogeneous integr ally \; closed ideals of A. DTEND;TZID=Europe/Zurich:20120413T120000 END:VEVENT BEGIN:VEVENT UID:news761@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T004459 DTSTART;TZID=Europe/Zurich:20120330T103000 SUMMARY:Seminar Algebra and Geometry: Alexandru Constantinescu (Universitä t Basel) DESCRIPTION:On h-vectors of matroids X-ALT-DESC:On h-vectors of matroids DTEND;TZID=Europe/Zurich:20120330T120000 END:VEVENT BEGIN:VEVENT UID:news762@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T004749 DTSTART;TZID=Europe/Zurich:20120316T103000 SUMMARY:Seminar Algebra and Geometry: Julie Déserti and Matey Mateev (Univ ersität Basel) DESCRIPTION:T.B.A. X-ALT-DESC:T.B.A. DTEND;TZID=Europe/Zurich:20120316T120000 END:VEVENT BEGIN:VEVENT UID:news763@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T004933 DTSTART;TZID=Europe/Zurich:20120309T103000 SUMMARY:Seminar Algebra and Geometry: Thomas Kahle (ETH Zürich) DESCRIPTION:In a polynomial ring\, a binomial says that two monomials are s calar multiples of each other.  Forgetting about the scalars\, a binomia l ideal describes an equivalence relation on the monoid of exponents.  \\r\\nIdeally one would want to carry out algebraic computations\, such as primary decomposition of binomial ideals\, entirely in this combinatoria l language.  We will present such a calculus\, enabling one to compute b y looking at pictures of monoids. X-ALT-DESC:In a polynomial ring\, a binomial says that two monomials are sc alar multiples of each other. \; Forgetting about the scalars\, a bin omial ideal describes an equivalence relation on the monoid of exponents.  \; \nIdeally one would want to carry out algebraic computations\, su ch as primary decomposition of binomial ideals\, entirely in this combina torial language. \; We will present such a calculus\, enabling one to compute by looking at pictures of monoids. DTEND;TZID=Europe/Zurich:20120309T120000 END:VEVENT BEGIN:VEVENT UID:news765@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T165841 DTSTART;TZID=Europe/Zurich:20111216T103000 SUMMARY:Seminar Algebra and Geometry: Paolo Mantero (Purdue University) DESCRIPTION:A vast part of literature on CI-linkage has addressed questions relative to the most relevant\, and well-behaved\, class of ideals in lin kage: licci ideals. However\, for a non-licci ideal I\, there are few resu lts describing the structure of the linkage class of I.In this talk we int roduce a theoretical definition for 'minimal' representatives in any even linkage class. We show that these idealsexist under reasonable assumptions on the linkage class\, and\, in general\, if they exist they are essentia lly unique.We then show that these ideals minimize homological invariants (e.g. Betti numbers\, multiplicity\, etc.) and they enjoy the best homolog ical and local properties among all the ideals in their even linkage class . This justifies why they are\, in some sense\, the `best' possible ideals in the even linkage class.We provide several classes of ideals that are t he minimal representatives of their even linkage classes (including determ inantal ideals) and\, if time permits\, show an easy application to produc e more evidence towards the Buchsbaum-Eisenbud-Horrocks Conjecture. X-ALT-DESC: A vast part of literature on CI-linkage has addressed questions relative to the most relevant\, and well-behaved\, class of ideals in lin kage: licci ideals. However\, for a non-licci ideal I\, there are few resu lts describing the structure of the linkage class of I.

In this talk we introduce a theoretical definition for 'minimal' representatives in any even linkage class. We show that these ideals
exist under reas onable assumptions on the linkage class\, and\, in general\, if they exist they are essentially unique.
We then show that these ideals minimize homological invariants (e.g. Betti numbers\, multiplicity\, etc.) and the y enjoy the best homological and local properties among all the ideals in their even linkage class. This justifies why they are\, in some sense\, th e `best' possible ideals in the even linkage class.

We provide several classes of ideals that are the minimal representatives of their ev en linkage classes (including determinantal ideals) and\, if time permits\ , show an easy application to produce more evidence towards the Buchsbaum- Eisenbud-Horrocks Conjecture. DTEND;TZID=Europe/Zurich:20111216T120000 END:VEVENT BEGIN:VEVENT UID:news766@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T170052 DTSTART;TZID=Europe/Zurich:20111209T103000 SUMMARY:Seminar Algebra and Geometry: Volkmar Welker (Philipps-Universität Marburg) DESCRIPTION:Generalized Inversion Statistics X-ALT-DESC:Generalized Inversion Statistics DTEND;TZID=Europe/Zurich:20111209T120000 END:VEVENT BEGIN:VEVENT UID:news767@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T170340 DTSTART;TZID=Europe/Zurich:20111202T103000 SUMMARY:Seminar Algebra and Geometry: Andriy Regeta (Technische Universitä t Kaiserslautern) DESCRIPTION:(joint work with A. Petravchuk and O. Iena)Let us consider the Lie algebra Wn=Wn(K) of all K-derivations of the polynomial ring K[x1\,... \,xn]. We discuss here a classof subalgebras in W2(K) over an algebraicall y closed field of characteristic zero. \\r\\nLet us consider natural actio n of the Lie algebra W2(K) on the field of rational functions K(x\,y). Rec all that every derivation Dof W2(K) of the ring K[x\,y] can be uniquely ex tended to a derivation of the field K(x\,y). It is natural to consider for afixed rational function u in K(x\,y)\\K the set A_{W2}(u) of all derivat ions D of W2 such that D(u)=0. This set is called the annihilatorof u in W 2(K). It is a Lie subalgebra of W2(K) and at the same time a K[x\,y]-submo dule of the K[x\,y]-module W2(K).We show that it is a free K[x\,y]-module of rank 1 and describe centralizers of elements and the maximal abelian su balgebras of theLie algebra A_{W2}(u). X-ALT-DESC:(joint work with A. Petravchuk and O. Iena)

Let us co nsider the Lie algebra Wn=Wn(K) of all K-derivations of the polynomial ring K[x1\,...\,xn]. We discuss h ere a class
of subalgebras in W2(K) over an algebraically closed field of characteristic zero.
\nLet us consider natural actio n of the Lie algebra W2(K) on the field of rational functions K (x\,y). Recall that every derivation D
of W2(K) of the rin g K[x\,y] can be uniquely extended to a derivation of the field K(x\,y). I t is natural to consider for a
fixed rational function u in K(x\,y)\\ K the set A_{W2}(u) of all derivations D of W2 such that D(u)=0. This set is called the annihilator
of u in W2 (K). It is a Lie subalgebra of W2(K) and at the same time a K[x \,y]-submodule of the K[x\,y]-module W2(K).

We show that it is a free K[x\,y]-module of rank 1 and describe centralizers of el ements and the maximal abelian subalgebras of the
Lie algebra A_{W2}(u). DTEND;TZID=Europe/Zurich:20111202T120000 END:VEVENT BEGIN:VEVENT UID:news768@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T170631 DTSTART;TZID=Europe/Zurich:20111118T103000 SUMMARY:Seminar Algebra and Geometry: Rafael Andrist (Universität Wupperta l) DESCRIPTION:A Danielewski surface is given as the hypersurface $x y = f(z)$ in $\\mathbb{C}^3$\, where $f$ is a polynomial with only simple zeroes. Such a surface enjoys the Density Property\, i.e. the Lie algebra gener ated by the complete holomorphic vector fields is dense in the Lie algeb ra of all holomorphic vector fields.In case of a Danielewski surface t he so-called overshear group is dense in the group of holomorphic automo rphisms. We describe the group structure of the overshear group with the help of Nevanlinna theory. X-ALT-DESC: A Danielewski surface is given as the hypersurface $x y = f(z)$ in $\\mathbb{C}^3$\, where $f$ is a polynomial with only simple zeroes. Such a surface enjoys the Density Property\, i.e. the Lie algebra gener ated by the complete holomorphic vector fields is dense in the Lie algeb ra of all holomorphic vector fields.

In case of a Danielewski surface the so-called overshear group is dense in the group of holomorp hic automorphisms. We describe the group structure of the overshear grou p with the help of Nevanlinna theory. DTEND;TZID=Europe/Zurich:20111118T120000 END:VEVENT BEGIN:VEVENT UID:news769@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T171244 DTSTART;TZID=Europe/Zurich:20111111T103000 SUMMARY:Seminar Algebra and Geometry: Winfried Bruns (Universität Osnabrü ck) DESCRIPTION:We report on joint work with Chr. Krattenthaler and J. Uliczka. Stanley decompositions of multigraded modules M over polynomials rings hav e been discussed intensively in recent years. There is a natural notion of depth that goes with a Stanley decomposition\, called the Stanley depth. Stanley conjectured that the Stanley depth of a module M is always at leas t the (classical) depth of M. We introduce a weaker type of decomposition\ , which we call Hilbert decomposition\, since it only depends on the Hilbe rt function of M\, and an analogous notion of depth\, called Hilbert depth . Since Stanley decompositions are Hilbert decompositions\, the latter set upper bounds to the existence of Stanley decompositions.The advantage of Hilbert decompositions is that they are easier to find.We test our new not ion on the syzygy modules of the residue class field of K[X1\,...\,Xn] (as usual identified with K). Writing M(n\,k) for the k-th syzygy module\, we show that the Hilbert depth of M(n\,1)\, namely the irrelevant maximal id eal\, is $\\lfloor(n+1)/2\\rfloor$. Furthermore\, we show that\, for $n > k \\ge \\lfloor n/2\\rfloor$\, the (multigraded) Hilbert depth of M(n\,k) is equal to n-1. We conjecture that the same holds for the Stanley depth. For the range n/2 > k > 1\, it seems impossible to come up with a compact formula for the Hilbert depth. Instead\, we provide very precise asymptoti c results as n becomes large.Related ideals are the powers of the irreleva nt maximal ideal. For them the (standard graded) Hilbert depth can be comp utedprecisely. X-ALT-DESC: We report on joint work with Chr. Krattenthaler and J. Uliczka.

Stanley decompositions of multigraded modules M over polynomia ls rings have been discussed intensively in recent years. There is a natur al notion of depth that goes with a Stanley decomposition\, called the Stanley depth. Stanley conjectured that the Stanley depth of a module M is always at least the (classical) depth of M. We introduce a weaker typ e of decomposition\, which we call Hilbert decomposition\, since it only depends on the Hilbert function of M\, and an analogous notion of de pth\, called Hilbert depth. Since Stanley decompositions are Hilber t decompositions\, the latter set upper bounds to the existence of Stanley decompositions.The advantage of Hilbert decompositions is that they are e asier to find.

We test our new notion on the syzygy modules of the residue class field of K[X1\,...\,Xn] (as usual identified with K). Writing M(n\,k) for the k-th syzygy module\, we show t hat the Hilbert depth of M(n\,1)\, namely the irrelevant maximal ideal\, i s $\\lfloor(n+1)/2\\rfloor$. Furthermore\, we show that\, for $n >\; k \ \ge \\lfloor n/2\\rfloor$\, the (multigraded) Hilbert depth of M(n\,k) is equal to n-1. We conjecture that the same holds for the Stanley depth. For the range n/2 >\; k >\; 1\, it seems impossible to come up with a com pact formula for the Hilbert depth. Instead\, we provide very precise asym ptotic results as n becomes large.

Related ideals are the power s of the irrelevant maximal ideal. For them the (standard graded) Hilbert depth can be computed
precisely. DTEND;TZID=Europe/Zurich:20111111T120000 END:VEVENT BEGIN:VEVENT UID:news770@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T171622 DTSTART;TZID=Europe/Zurich:20111104T000000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft and Maria Fernanda Ro bayo (Universität Basel)\, Two 30 minutes talks DESCRIPTION:T.B.A. X-ALT-DESC:T.B.A. END:VEVENT BEGIN:VEVENT UID:news771@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T171920 DTSTART;TZID=Europe/Zurich:20111028T000000 SUMMARY:Seminar Algebra and Geometry: Naihuan Jing (North Carolina State Un iv. and South China Univ. of Technology) DESCRIPTION:Exactly 100 years ago Schur constructed irreducible characters of the spin groups of the symmetric group and introduced the famous Schur Q-functions. Using ideas from affine Lie algebras and McKay corresponde nce\, Frenkel\, Jing and Wang fixed the irreducible characters for the sp in group of the wreath products for the symmetric group without knowing t he complete character table. In this work we will generalize Schur's work and completely determine all character values for the spin wreath produc ts in type A case. This is joint work with X. Hu. X-ALT-DESC: Exactly 100 years ago Schur constructed irreducible characters of the spin groups of the symmetric group and introduced the famous Schur Q-functions. Using ideas from affine Lie algebras and McKay corresponde nce\, Frenkel\, Jing and Wang fixed the irreducible characters for the sp in group of the wreath products for the symmetric group without knowing t he complete character table. In this work we will generalize Schur's work and completely determine all character values for the spin wreath produc ts in type A case. This is joint work with X. Hu. END:VEVENT BEGIN:VEVENT UID:news772@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T172107 DTSTART;TZID=Europe/Zurich:20111021T000000 SUMMARY:Seminar Algebra and Geometry: Émilie Dufresne and Jérémy Blanc ( Universität Basel)\, Two 30 minutes talks DESCRIPTION:T.B.A. X-ALT-DESC:T.B.A. END:VEVENT BEGIN:VEVENT UID:news773@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T172233 DTSTART;TZID=Europe/Zurich:20111014T000000 SUMMARY:Seminar Algebra and Geometry: Alexandru Constantinescu and Pierre-M arie Poloni (Universität Basel)\, Two 30 minutes talks DESCRIPTION:T.B.A. X-ALT-DESC:T.B.A. END:VEVENT BEGIN:VEVENT UID:news774@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T172423 DTSTART;TZID=Europe/Zurich:20111007T000000 SUMMARY:Seminar Algebra and Geometry: Bruno Duchesne (The Hebrew University of Jerusalem) DESCRIPTION:Symmetric spaces of non-compact type (which are simply-connecte d Riemannian manifolds of non-positive curvature with a geodesic symmetr y at each point) are classical and useful geometric tools to understand finite-dimensional linear representations of groups.\\r\\nWe will look at some infinite dimensional symmetric spaces of non-positive curvature which have a remarkable property : they have finite rank. There exists a positive integer p such that any isometrically embedded Euclidean spac e has dimension at most p.\\r\\nThe talk will be focused on the properti es of these spaces and some group actions which come from (non-unitary) infinite-dimensional representations. X-ALT-DESC:Symmetric spaces of non-compact type (which are simply-connected Riemannian manifolds of non-positive curvature with a geodesic symmetry at each point) are classical and useful geometric tools to understand finite-dimensional linear representations of groups.\nWe will look at s ome infinite dimensional symmetric spaces of non-positive curvature whic h have a remarkable property : they have finite rank. There exists a pos itive integer p such that any isometrically embedded Euclidean space has dimension at most p.\nThe talk will be focused on the properties of the se spaces and some group actions which come from (non-unitary) infinite- dimensional representations. END:VEVENT BEGIN:VEVENT UID:news775@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T172550 DTSTART;TZID=Europe/Zurich:20110930T000000 SUMMARY:Seminar Algebra and Geometry: Tommy Wuxing Cai (Universität Basel) DESCRIPTION:We first realize Jack function of rectangular shapes. Then we introduce an iterative method to realize Jack functions of general shape s from those of rectangular shapes. As a byproduct\, we prove some speci al cases of Richard P. Stanley's conjecture about the positivity of the Littlewood-Richardson coefficients of Jack functions.Contents: 1. partiti ons and symmetric functions 2. Some history and questions about symmetric functions 3. Vertex operator realization of rectangular Jack functions 4. A special case of Stanley's conjecture and the realization of general Jack functions 5. Open questions X-ALT-DESC:We first realize Jack function of rectangular shapes. Then we i ntroduce an iterative method to realize Jack functions of general shapes from those of rectangular shapes. As a byproduct\, we prove some specia l cases of Richard P. Stanley's conjecture about the positivity of the Littlewood-Richardson coefficients of Jack functions.

Contents:
1. partitions and symmetric functions
2. Some history and que stions about symmetric functions
3. Vertex operator realization of r ectangular Jack functions
4. A special case of Stanley's conjecture and the realization of general Jack functions
5. Open questions END:VEVENT BEGIN:VEVENT UID:news776@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T172827 DTSTART;TZID=Europe/Zurich:20110527T000000 SUMMARY:Seminar Algebra and Geometry: Olivier Serman (Université Lille 1) DESCRIPTION:Moduli spaces of principal bundles on curves\, which have been introduced as non-abelian analogs of the Jacobian variety\, carry a very rich geometry. In this talk I will focus on the singularities of these v arieties. I will show how local factoriality of GIT quotients can be used to give a description of their singular locus\, and then compute the fun damental group of the smooth locus of these moduli spaces. X-ALT-DESC: Moduli spaces of principal bundles on curves\, which have been introduced as non-abelian analogs of the Jacobian variety\, carry a very rich geometry. In this talk I will focus on the singularities of these v arieties. I will show how local factoriality of GIT quotients can be used to give a description of their singular locus\, and then compute the fun damental group of the smooth locus of these moduli spaces. END:VEVENT BEGIN:VEVENT UID:news777@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T180652 DTSTART;TZID=Europe/Zurich:20110520T000000 SUMMARY:Seminar Algebra and Geometry: Émilie Dufresne (Universität Basel) DESCRIPTION:Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an aff ine algebraic variety is not always finitely generated. In some sense\, h owever\, invariant rings are not far from being affine. Indeed\, invarian t rings are always quasi-affine\, and finite separating sets always exist . We give a new method for finding a quasi-affine variety on which the ri ng of regular functions is equal to a given invariant ring\, and give a criterion to recognize separating algebras. We use the method and criteri on to construct new examples. X-ALT-DESC: Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an aff ine algebraic variety is not always finitely generated. In some sense\, h owever\, invariant rings are not far from being affine. Indeed\, invarian t rings are always quasi-affine\, and finite separating sets always exist . We give a new method for finding a quasi-affine variety on which the ri ng of regular functions is equal to a given invariant ring\, and give a criterion to recognize separating algebras. We use the method and criteri on to construct new examples. END:VEVENT BEGIN:VEVENT UID:news778@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T180831 DTSTART;TZID=Europe/Zurich:20110516T160000 SUMMARY:Seminar Algebra and Geometry: Aldo Conca (University of Genova) DESCRIPTION:The goal of the talk is to explain recent results and conjectur es regarding Koszul algebras and their syzygies. Koszul algebras are  g raded K-algebras R such that the residue filed K has a linear R-free res olution. Koszul algebras are defined by quadrics.  But not all algebras defined by quadric are Koszul. However many classical algebras defined b y quadrics  (e.g. the coordinate ring of the Grassmannian in its standa rd embedding)  are Koszul.The main idea I will discuss is that  the sy zygies of Koszul algebras have some properties in common with the syzygi es of algebras defined by monomialsof degree two. X-ALT-DESC: The goal of the talk is to explain recent results and conjectur es regarding Koszul algebras and their syzygies. Koszul algebras are  \; graded K-algebras R such that the residue filed K has a linear R-free resolution. Koszul algebras are defined by quadrics. \; But not all algebras defined by quadric are Koszul. However many classical algebras defined by quadrics \; (e.g. the coordinate ring of the Grassmannian in its standard embedding) \; are Koszul.
The main idea I will discuss is that \; the syzygies of Koszul algebras have some proper ties in common with the syzygies of algebras defined by monomials
of degree two. DTEND;TZID=Europe/Zurich:20110516T170000 END:VEVENT BEGIN:VEVENT UID:news779@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T181018 DTSTART;TZID=Europe/Zurich:20110513T000000 SUMMARY:Seminar Algebra and Geometry: Ivan Arzhantsev (Moscow State Univers ity and Institut Fourier) DESCRIPTION:(joint work with Devrim Celik and Juergen Hausen)We begin with a survey of known results concerning categorical quotients.Given an actio n of an affine algebraic group with only trivial characters on a factoria l variety\, we characterize existence of categorical quotient in the cate gory of algebraic varieties. Moreover\, allowing constructible sets as qu otients\, we obtain a more general existence result\, which\, for example \, settles the case of a finitely generated algebra of invariants. As an application\, we provide a combinatorial GIT-type construction of categor ial quotients for actions on\, e.g. complete\, varieties with finitely ge nerated Cox ring via lifting to the universal torsor. X-ALT-DESC: (joint work with Devrim Celik and Juergen Hausen)

We begin with a survey of known results concerning categorical quotients.
Given an action of an affine algebraic group with only trivial charact ers on a factorial variety\, we characterize existence of categorical quo tient in the category of algebraic varieties. Moreover\, allowing constr uctible sets as quotients\, we obtain a more general existence result\, w hich\, for example\, settles the case of a finitely generated algebra of invariants. As an application\, we provide a combinatorial GIT-type const ruction of categorial quotients for actions on\, e.g. complete\, varietie s with finitely generated Cox ring via lifting to the universal torsor. END:VEVENT BEGIN:VEVENT UID:news780@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T181256 DTSTART;TZID=Europe/Zurich:20110506T000000 SUMMARY:Seminar Algebra and Geometry: Andreas Maurischat (Universität Heid elberg) DESCRIPTION:In Hopf-Galois theory one can attach a Hopf algebra H (resp.   an affine group scheme G=Spec(H) ) to any finite field extension. In gene ral\, however\, this Hopf-algebra is not unique\, but in some cases - e.g . normal separable extensions - there are natural choices. In this talk\ , we will show how one can obtain "natural choices" for finite extensions (even inseparable ones) by imposing an extra structure on the field\, na mely a so-called iterative derivation. X-ALT-DESC: In Hopf-Galois theory one can attach a Hopf algebra H (resp. &n bsp\;an affine group scheme G=Spec(H) ) to any finite field extension. In general\, however\, this Hopf-algebra is not unique\, but in some cases - e.g. normal separable extensions - there are natural choices. In this talk\, we will show how one can obtain "\;natural choices"\; for f inite extensions (even inseparable ones) by imposing an extra structure o n the field\, namely a so-called iterative derivation. END:VEVENT BEGIN:VEVENT UID:news781@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T181459 DTSTART;TZID=Europe/Zurich:20110429T000000 SUMMARY:Seminar Algebra and Geometry: Matteo Varbaro (University of Genova) DESCRIPTION:T.B.A. X-ALT-DESC:T.B.A. END:VEVENT BEGIN:VEVENT UID:news782@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T181619 DTSTART;TZID=Europe/Zurich:20110415T000000 SUMMARY:Seminar Algebra and Geometry: Abraham Broer (Université de Montré al) DESCRIPTION:Cohomology of line bundles on the cotangent bundle of a complet e homogeneous space X-ALT-DESC:Cohomology of line bundles on the cotangent bundle of a complete homogeneous space END:VEVENT BEGIN:VEVENT UID:news783@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T181851 DTSTART;TZID=Europe/Zurich:20110408T000000 SUMMARY:Seminar Algebra and Geometry: Enrico Schlesinger (Politecnico di Mi lano) DESCRIPTION:Grothendieck has constructed the Hilbert scheme  that parametr izes all subschemes of PN with a given Hilbert polynomial\, and Hartshorne in his thesis has shown that it is connected. For a  curve in P3 the Hil bert polynomial is given by the degree d and by the arithmetic genus g. I will explain why\, even if one is primarily interested in smooth curves\ , the correct class of curve to look at is that of locally Cohen Macaulay curves. These are parametrized by an open subscheme Hd\,g of the full Hil bert scheme.It is an open question whether Hd\,g is connected whenever non empty. This question was motivated by a result by Martin-Deschamps and Per rin: they showed that Hd\,g always has an irreducible component made up by "extremal curves"\; these curves have the largest cohomology among curves in Hd\,g. So there is no obstruction from semicontinuity that prevents t he possibility that any smooth curve be specialized to an extremal curve. I will discuss the state of affairs about this question\, and briefly de scribe work in progress (with the help of Macaulay 2) showing that curves of type (a\,a+4) on a smooth quadric surface are in the connected compon ent of extremal curves\; this problem was  raised in Hartshorne's papers    "On the connectedness of the Hilbert scheme of curves in P3" Comm. Al g. 28\, 2000  and "Questions of connectedness of the Hilbert scheme of cu rves in P3" in the volume for Abhyankar's 70th (2004)\, and was still on the open problems list of the Workshop "Components of the Hilbert Schemes " (AIM Palo Alto 2010). X-ALT-DESC: Grothendieck has constructed the Hilbert scheme \; that par ametrizes all subschemes of PN with a given Hilbert polynomial\ , and Hartshorne in his thesis has shown that it is connected. For a \ ; curve in P3 the Hilbert polynomial is given by the degree d and by the arithmetic genus g. I will explain why\, even if one is primarily interested in smooth curves\, the correct class of curve to look at is that of locally Cohen Macaulay curves. These are parametri zed by an open subscheme Hd\,g of the full Hilbert schem e.

It is an open question whether Hd\,g is co nnected whenever nonempty. This question was motivated by a result by Mart in-Deschamps and Perrin: they showed that Hd\,g always h as an irreducible component made up by "\;extremal curves"\;\; the se curves have the largest cohomology among curves in Hd\,g< /i>. So there is no obstruction from semicontinuity that prevents the po ssibility that any smooth curve be specialized to an extremal curve.

I will discuss the state of affairs about this question\, and brief ly describe work in progress (with the help of Macaulay 2) showing that curves of type (a\,a+4) on a smooth quadric surface are in the connected component of extremal curves\; this problem was \; raised in Hartshorn e's papers \; \; "\;On the connectedness of the Hilbert schem e of curves in P3"\; Comm. Alg. 28\, 2000 \; and "\ ;Questions of connectedness of the Hilbert scheme of curves in P3"\; in the volume for Abhyankar's 70th (2004)\, and was still on th e open problems list of the Workshop "\;Components of the Hilbert Sch emes"\; (AIM Palo Alto 2010). END:VEVENT BEGIN:VEVENT UID:news784@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T182036 DTSTART;TZID=Europe/Zurich:20110401T000000 SUMMARY:Seminar Algebra and Geometry: Lucas Fresse (Hebrew University of Je rusalem) DESCRIPTION:To a nilpotent element x in a reductive Lie algebra\, one can a ttach several algebraic varieties which play roles in representation theo ry: its nilpotent orbit\; the intersection of its nilpotent orbit with a Borel subalgebra (the irreducible components of this intersection are ca lled orbital varieties)\; the fiber over x of the Springer resolution. Th ere is a close relation between the Springer fiber over x and the orbital varieties attached to x. In this talk\, we rely on this relation in orde r to study two properties of orbital varieties: the smoothness\, and the property to contain a dense B-orbit. We concentrate on type A. We provide several criteria which suggest that the two mentioned properties are re lated. This is a joint work with Anna Melnikov. X-ALT-DESC: To a nilpotent element x in a reductive Lie algebra\, one can a ttach several algebraic varieties which play roles in representation theo ry: its nilpotent orbit\; the intersection of its nilpotent orbit with a Borel subalgebra (the irreducible components of this intersection are ca lled orbital varieties)\; the fiber over x of the Springer resolution. Th ere is a close relation between the Springer fiber over x and the orbital varieties attached to x. In this talk\, we rely on this relation in orde r to study two properties of orbital varieties: the smoothness\, and the property to contain a dense B-orbit. We concentrate on type A. We provide several \;criteria which suggest that the two mentioned properties a re related. This is a joint work with Anna Melnikov. END:VEVENT BEGIN:VEVENT UID:news785@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T182557 DTSTART;TZID=Europe/Zurich:20110311T000000 SUMMARY:Seminar Algebra and Geometry: Marc Chardin (Institut Mathématique de Jussieu\, Paris) DESCRIPTION:In this lecture\, I will present a way of computing the image o f a  rational map using a free resolution of the symmetric algebra. In t his setting\, the  method was initiated by Jean-Pierre Jouanolou\, and f urther developed by him\, by Laurent  Busé and by myself. The origin of this method is the work of people in Geometric  Modeling\, motivated by a simple question: how to represent the  intersection of two surfaces parametrized by rational functions? \\r\\nTheir approach was first put on firm mathematical bases by David Cox and several collaborators. The key   point in this approach is to control the torsion in the symmetric alge bra. This is performed using a construction of Herzog\, Simis and Vasconc elos\, that gives information on the equations of Rees algebras. X-ALT-DESC:In this lecture\, I will present a way of computing the image of a \; rational map using a free resolution of the symmetric algebra. In this setting\, the \; method was initiated by Jean-Pierre Jouanolo u\, and further developed by him\, by Laurent \; Busé and by myself. The origin of this method is the work of people in Geometric \; Mode ling\, motivated by a simple question: how to represent the \; inters ection of two surfaces parametrized by rational functions? \nTheir appro ach was first put on firm mathematical bases by David Cox and several col laborators. The key \; point in this approach is to control the torsi on in the symmetric algebra. This is performed using a construction of He rzog\, Simis and Vasconcelos\, that gives information on the equations of Rees algebras. END:VEVENT BEGIN:VEVENT UID:news786@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T182857 DTSTART;TZID=Europe/Zurich:20110304T000000 SUMMARY:Seminar Algebra and Geometry: Nathan Ilten (Max Planck Institute) DESCRIPTION:A p-divisor on a normal variety Y is a divisor satisfying some positivity properties\, where the usual integral or rational coefficients have been replaced by polyhedral coeffi- cients. K. Altmann and J. Haus en have shown that there is a correspondence between p-divisors and affin e T-varieties\, i.e. normal varieties together with some effective torus action. Given some T-variety X\, one can try to ”upgrade” the torus a ction by considering some larger torus acting on X\, or ”downgrade” th e torus action by considering the action of some subtorus. I will discuss how these upgrading and downgrading procedures change the corresponding p-divisors. Time permitting\, I will present an application of the upgra de procedure dealing with the p-divisors of Cox rings of certain T-variet ies. This is joint work with R. Vollmert. X-ALT-DESC: A p-divisor on a normal variety Y is a divisor satisfying some positivity properties\, where the usual integral or rational coefficients have been replaced by polyhedral coeffi- cients. K. Altmann and J. Haus en have shown that there is a correspondence between p-divisors and affin e T-varieties\, i.e. normal varieties together with some effective torus action. Given some T-variety X\, one can try to ”upgrade” the torus a ction by considering some larger torus acting on X\, or ”downgrade” th e torus action by considering the action of some subtorus. I will discuss how these upgrading and downgrading procedures change the corresponding p-divisors. Time permitting\, I will present an application of the upgra de procedure dealing with the p-divisors of Cox rings of certain T-variet ies. This is joint work with R. Vollmert. END:VEVENT BEGIN:VEVENT UID:news787@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T183147 DTSTART;TZID=Europe/Zurich:20110225T000000 SUMMARY:Seminar Algebra and Geometry: Jérôme Tambour (Université de Bour gogne) DESCRIPTION:It is not easy to construct examples of non k ̈ahler compact complex manifold. For instance\, every algebraic variety\, and every Riem ann surface\, is ka ̈hler. The classical examples of such varieties are Hopf manifolds (1948) and Calabi-Eckmann manifolds (1953) which are compl ex structures on product of spheres Sp × Sq (with p and q odd). Santiag o Lopez de Medrano\, Alberto Verjovsky and Laurent Meersseman gave a gene ralization of this construction. The interest of theirs manifolds\, known as LVM manifolds\, stand in the fact that it is practical to compute som e of their topological invariants (homology and cohomology for example). They are also endowed with a very nice action of a compact torus.\\r\\nTh e talk will mainly deal with a generalization due to Bosio of the LVM man ifolds\, emphazing the combinatorial aspect of the LVM manifolds. These n ew manifolds are known as LVMB manifolds. In particular\, our aim will be to show the very strong connection between LVMB manifolds\, toric variet ies and triangulations of spheres. X-ALT-DESC:It is not easy to construct examples of non k ̈ahler compact c omplex manifold. For instance\, every algebraic variety\, and every Riema nn surface\, is ka ̈hler. The classical examples of such varieties are H opf manifolds (1948) and Calabi-Eckmann manifolds (1953) which are comple x structures on product of spheres Sp × Sq (with p and q odd). Santiago Lopez de Medrano\, Alberto Verjovsky and Laurent Meersseman gave a gener alization of this construction. The interest of theirs manifolds\, known as LVM manifolds\, stand in the fact that it is practical to compute some of their topological invariants (homology and cohomology for example). T hey are also endowed with a very nice action of a compact torus.\nThe tal k will mainly deal with a generalization due to Bosio of the LVM manifold s\, emphazing the combinatorial aspect of the LVM manifolds. These new ma nifolds are known as LVMB manifolds. In particular\, our aim will be to s how the very strong connection between LVMB manifolds\, toric varieties a nd triangulations of spheres. END:VEVENT BEGIN:VEVENT UID:news788@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T183730 DTSTART;TZID=Europe/Zurich:20101217T000000 SUMMARY:Seminar Algebra and Geometry: Bruno Benedetti (Technische Universit ät Berlin) DESCRIPTION:Shelling\, constructing\, counting X-ALT-DESC:Shelling\, constructing\, counting END:VEVENT BEGIN:VEVENT UID:news789@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T200532 DTSTART;TZID=Europe/Zurich:20101210T000000 SUMMARY:Seminar Algebra and Geometry: Martin Kohls (Technische Universität München) DESCRIPTION:Separating invariants for the basic $G_a$-actions X-ALT-DESC:Separating invariants for the basic $G_a$-actions END:VEVENT BEGIN:VEVENT UID:news790@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T200506 DTSTART;TZID=Europe/Zurich:20101203T000000 SUMMARY:Seminar Algebra and Geometry: Alexandru Constantinescu (Universitä t Basel) DESCRIPTION:Parametrizations of Ideals in K[x\,y] X-ALT-DESC:Parametrizations of Ideals in K[x\,y] END:VEVENT BEGIN:VEVENT UID:news791@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T200642 DTSTART;TZID=Europe/Zurich:20101119T000000 SUMMARY:Seminar Algebra and Geometry: Gavin Brown (Loughborough University) DESCRIPTION:Gorenstein projections and diptych varieties X-ALT-DESC:Gorenstein projections and diptych varieties END:VEVENT BEGIN:VEVENT UID:news792@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T200734 DTSTART;TZID=Europe/Zurich:20101112T000000 SUMMARY:Seminar Algebra and Geometry: Claudia R. Alcantara (Universidad de Guanajuato\, Mexico) DESCRIPTION:Holomorphic foliations on CP2 and Geometric Invariant Theory X-ALT-DESC:Holomorphic foliations on CP2 and Geometric Invariant Theory END:VEVENT BEGIN:VEVENT UID:news793@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T200859 DTSTART;TZID=Europe/Zurich:20101105T000000 SUMMARY:Seminar Algebra and Geometry: Stéphane Lamy (University of Warwick / Université Lyon 1) DESCRIPTION:Birational constructions of automorphisms of affine 3-folds X-ALT-DESC:Birational constructions of automorphisms of affine 3-folds END:VEVENT BEGIN:VEVENT UID:news794@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T201001 DTSTART;TZID=Europe/Zurich:20101029T000000 SUMMARY:Seminar Algebra and Geometry: Markus Brodmann (Universität Zürich ) DESCRIPTION:Projective Varieties of Low Degree X-ALT-DESC:Projective Varieties of Low Degree END:VEVENT BEGIN:VEVENT UID:news795@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T201207 DTSTART;TZID=Europe/Zurich:20101022T000000 SUMMARY:Seminar Algebra and Geometry: Alvaro Liendo (Universität Basel) DESCRIPTION:Normal singularities with torus actions X-ALT-DESC:Normal singularities with torus actions END:VEVENT BEGIN:VEVENT UID:news796@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T201336 DTSTART;TZID=Europe/Zurich:20101015T000000 SUMMARY:Seminar Algebra and Geometry: Émilie Dufresne (Universität Basel) DESCRIPTION:Additive group actions in positive chracteristic X-ALT-DESC:Additive group actions in positive chracteristic END:VEVENT BEGIN:VEVENT UID:news797@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T201608 DTSTART;TZID=Europe/Zurich:20100929T140000 SUMMARY:Seminar Algebra and Geometry: Frédéric Mangolte (Université d'An gers) DESCRIPTION:Algebraic approximations of diffeomorphisms of surfaces X-ALT-DESC:Algebraic approximations of diffeomorphisms of surfaces DTEND;TZID=Europe/Zurich:20100929T153000 END:VEVENT BEGIN:VEVENT UID:news798@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T201826 DTSTART;TZID=Europe/Zurich:20100924T000000 SUMMARY:Seminar Algebra and Geometry: Hamid Ahmadinezhad (Universität Base l) DESCRIPTION:On rigidity of low degree del Pezzo fibrations X-ALT-DESC:On rigidity of low degree del Pezzo fibrations END:VEVENT BEGIN:VEVENT UID:news809@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T212605 DTSTART;TZID=Europe/Zurich:20100528T110000 SUMMARY:Seminar Algebra and Geometry: Guillaume Batog (Université de Nancy ) DESCRIPTION:Using polynomial invariants to compute geometric predicates X-ALT-DESC:Using polynomial invariants to compute geometric predicates DTEND;TZID=Europe/Zurich:20100528T123000 END:VEVENT BEGIN:VEVENT UID:news808@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T212410 DTSTART;TZID=Europe/Zurich:20100528T093000 SUMMARY:Seminar Algebra and Geometry: Jan Draisma (Eindhoven University of Technology) DESCRIPTION:A tropical proof of the Brill-Noether theorem X-ALT-DESC:A tropical proof of the Brill-Noether theorem DTEND;TZID=Europe/Zurich:20100528T103000 END:VEVENT BEGIN:VEVENT UID:news807@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T212027 DTSTART;TZID=Europe/Zurich:20100521T000000 SUMMARY:Seminar Algebra and Geometry: Jerzy Weyman (Northeastern Universit y) DESCRIPTION:Quivers and saturation for tensor products multiplicities for c lassical groups X-ALT-DESC:Quivers and saturation for tensor products multiplicities for cl assical groups END:VEVENT BEGIN:VEVENT UID:news806@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T211443 DTSTART;TZID=Europe/Zurich:20100430T000000 SUMMARY:Seminar Algebra and Geometry: Maria Evelina Rossi (University of Ge noa) DESCRIPTION:Isomorphism classes of Gorenstein local rings via Macaulay's in verse system X-ALT-DESC:Isomorphism classes of Gorenstein local rings via Macaulay's inv erse system END:VEVENT BEGIN:VEVENT UID:news805@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202904 DTSTART;TZID=Europe/Zurich:20100423T000000 SUMMARY:Seminar Algebra and Geometry: Tanja Becker (Universität Mainz) DESCRIPTION:Beispiel eines Sl_2-Hilbertschemas X-ALT-DESC:Beispiel eines Sl_2-Hilbertschemas END:VEVENT BEGIN:VEVENT UID:news804@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202808 DTSTART;TZID=Europe/Zurich:20100416T110000 SUMMARY:Seminar Algebra and Geometry: Zinovy Reichstein (University of Brit ish Columbia) DESCRIPTION:Versal actions with a twist X-ALT-DESC:Versal actions with a twist DTEND;TZID=Europe/Zurich:20100416T120000 END:VEVENT BEGIN:VEVENT UID:news803@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202654 DTSTART;TZID=Europe/Zurich:20100416T093000 SUMMARY:Seminar Algebra and Geometry: Alvaro Liendo (Université de Grenobl e) DESCRIPTION:A birational characterization of affine varieties with trivial ML invariant X-ALT-DESC:A birational characterization of affine varieties with trivial M L invariant DTEND;TZID=Europe/Zurich:20100416T103000 END:VEVENT BEGIN:VEVENT UID:news802@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202456 DTSTART;TZID=Europe/Zurich:20100409T000000 SUMMARY:Seminar Algebra and Geometry: Michel Brion (Université Joseph Four ier Grenoble) DESCRIPTION:Picard groups of homogeneous varieties X-ALT-DESC:Picard groups of homogeneous varieties END:VEVENT BEGIN:VEVENT UID:news801@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202321 DTSTART;TZID=Europe/Zurich:20100326T000000 SUMMARY:Seminar Algebra and Geometry: Jérémy Blanc (Universität Basel) DESCRIPTION:Algebraic actions on the affine plane X-ALT-DESC:Algebraic actions on the affine plane END:VEVENT BEGIN:VEVENT UID:news800@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202200 DTSTART;TZID=Europe/Zurich:20100312T140000 SUMMARY:Seminar Algebra and Geometry: Luc Guyot (University of Göttingen) DESCRIPTION:Limits of metabelian groups X-ALT-DESC:Limits of metabelian groups DTEND;TZID=Europe/Zurich:20100312T153000 END:VEVENT BEGIN:VEVENT UID:news799@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T202010 DTSTART;TZID=Europe/Zurich:20100305T000000 SUMMARY:Seminar Algebra and Geometry: Ulrich Derenthal (University of Freib urg) DESCRIPTION:Rational points on cubic surfaces X-ALT-DESC:Rational points on cubic surfaces END:VEVENT BEGIN:VEVENT UID:news820@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T220426 DTSTART;TZID=Europe/Zurich:20091218T000000 SUMMARY:Seminar Algebra and Geometry: Hanspeter Kraft (Basel University) DESCRIPTION:Was ist ein Faserbündel? X-ALT-DESC:Was ist ein Faserbündel? END:VEVENT BEGIN:VEVENT UID:news819@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T220304 DTSTART;TZID=Europe/Zurich:20091211T000000 SUMMARY:Seminar Algebra and Geometry: Pierre-Marie Poloni (Basel University ) DESCRIPTION:Some examples coming from the study of the Danielewski hypersur faces X-ALT-DESC:Some examples coming from the study of the Danielewski hypersurf aces END:VEVENT BEGIN:VEVENT UID:news818@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T220207 DTSTART;TZID=Europe/Zurich:20091204T000000 SUMMARY:Seminar Algebra and Geometry: Roland Lötscher (Basel University) DESCRIPTION:Essential dimension of algebraic tori X-ALT-DESC:Essential dimension of algebraic tori END:VEVENT BEGIN:VEVENT UID:news817@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T220108 DTSTART;TZID=Europe/Zurich:20091120T000000 SUMMARY:Seminar Algebra and Geometry: Maike Massierer (Basel University) DESCRIPTION:Aspects of class field theory for global function fields X-ALT-DESC:Aspects of class field theory for global function fields END:VEVENT BEGIN:VEVENT UID:news816@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T215928 DTSTART;TZID=Europe/Zurich:20091113T000000 SUMMARY:Seminar Algebra and Geometry: Jean-Philippe Furter (Université de La Rochelle) DESCRIPTION:Normal subgroup generated by a plane polynomial automorphism X-ALT-DESC:Normal subgroup generated by a plane polynomial automorphism END:VEVENT BEGIN:VEVENT UID:news815@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T215827 DTSTART;TZID=Europe/Zurich:20091106T000000 SUMMARY:Seminar Algebra and Geometry: Elisa Gorla (Basel University) DESCRIPTION:Gorestein Liaison and determinantal schemes X-ALT-DESC:Gorestein Liaison and determinantal schemes END:VEVENT BEGIN:VEVENT UID:news814@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T213610 DTSTART;TZID=Europe/Zurich:20091030T000000 SUMMARY:Seminar Algebra and Geometry: Immanuel Stampfli (Basel University) DESCRIPTION:Some aspects of A^1-bundles X-ALT-DESC:Some aspects of A^1-bundles END:VEVENT BEGIN:VEVENT UID:news813@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T213354 DTSTART;TZID=Europe/Zurich:20091016T000000 SUMMARY:Seminar Algebra and Geometry: Stéphane Vénéreau (Basel Universit y) DESCRIPTION:On the Bhatwadekar-Dutta-Berson-Vénéreau Polynomials X-ALT-DESC:On the Bhatwadekar-Dutta-Berson-Vénéreau Polynomials END:VEVENT BEGIN:VEVENT UID:news812@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T213139 DTSTART;TZID=Europe/Zurich:20091009T000000 SUMMARY:Seminar Algebra and Geometry: Jonas Budmiger (Basel University) DESCRIPTION:An open problem on the coordinate ring of a variety with group action X-ALT-DESC:An open problem on the coordinate ring of a variety with group a ction END:VEVENT BEGIN:VEVENT UID:news811@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T213026 DTSTART;TZID=Europe/Zurich:20091002T000000 SUMMARY:Seminar Algebra and Geometry: Jacopo Gandini (University of Rome 1) DESCRIPTION:Spherical orbit closures in simple projective spaces and their normalization X-ALT-DESC:Spherical orbit closures in simple projective spaces and their n ormalization END:VEVENT BEGIN:VEVENT UID:news810@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20190212T212851 DTSTART;TZID=Europe/Zurich:20090925T000000 SUMMARY:Seminar Algebra and Geometry: Matey Mateev (Humboldt-Universität z u Berlin) DESCRIPTION:A sufficient criterion for the asymptotic stability of depths o f ideal transformed Rees-modules X-ALT-DESC:A sufficient criterion for the asymptotic stability of depths of ideal transformed Rees-modules END:VEVENT END:VCALENDAR