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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
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