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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 → <b>C</b><sup>m</sup> are al
 gebraically equivalent\, i.e.  whether there exists an algebraic automorph
 ism φ of <b>C</b><sup>m</sup> 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 → <b>C</b><sup>m<
 /sup> are algebraic embeddings and 2 dimX+ 1≤m\, then there exists a hol
 omorphic automorphism φ of <b>C</b><sup>m</sup> 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 <b>C</b> into <b>C</b><sup>3<
 /sup> are holomorphically equivalent.  In the course of this talk\,  we di
 scuss this idea.  Moreover\,  we provide examples of algebraic embeddings 
 into <b>C</b><sup>m</sup> that are holomorphically non-equivalent.
DTEND;TZID=Europe/Zurich:20141114T120000
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