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SUMMARY:Nathan Chen (Columbia University)
DTSTART:20230310T220000Z
DTEND:20230310T230000Z
DTSTAMP:20260407T214817Z
UID:agstanford/115
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 15/">Fano hypersurfaces and differential forms via positive characteristic
 </a>\nby Nathan Chen (Columbia University) as part of Stanford algebraic g
 eometry seminar\n\nLecture held in 383-N.\n\nAbstract\nHolomorphic forms a
 re an important birational invariant for studying the geometry of a variet
 y. In characteristic 0\, Fano varieties do not have any holomorphic forms.
  Surprisingly\, Kollár showed that in positive characteristic certain (si
 ngular) Fano varieties admit many global (n-1)-forms\, and he combined thi
 s with a specialization method to prove nonrationality of many complex Fan
 o hypersurfaces. In this talk\, we will revisit this construction and use 
 it to address several related questions for Fano hypersurfaces in certain 
 ranges: (1) how can one further measure their nonrationality\, (2) what ar
 e their possible rational endomorphisms\, and (3) is their birational auto
 morphism group infinite or finite? Parts of this will be joint with David 
 Stapleton as well as with Lena Ji-Stapleton.\n
LOCATION:https://researchseminars.org/talk/agstanford/115/
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