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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.  <br />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.<br />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
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