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SUMMARY:Nathan Chen (Columbia University)
DTSTART;VALUE=DATE-TIME:20230310T220000Z
DTEND;VALUE=DATE-TIME:20230310T230000Z
DTSTAMP;VALUE=DATE-TIME:20231130T082253Z
UID:agstanford/115
DESCRIPTION:Title: Fano hypersurfaces and differential forms via positive characteristic
\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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