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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.<br /> 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.<br /> 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.<br /> This is a joint work in progress wit
 h Jérémy Blanc.
DTEND;TZID=Europe/Zurich:20180403T120000
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