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SUMMARY:Louis Esser (UCLA)
DTSTART;VALUE=DATE-TIME:20211203T200000Z
DTEND;VALUE=DATE-TIME:20211203T210000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062719Z
UID:agstanford/71
DESCRIPTION:Title: Varieties of general type with doubly exponential asymptotics\nby
Louis Esser (UCLA) as part of Stanford algebraic geometry seminar\n\n\nAbs
tract\nBy a theorem of Haconâ€“McKernan\, Takayama\, and Tsuji\, for every
$n$ there is a constant $r_n$ for which every smooth variety $X$ of dimen
sion $n$ of general type has birational pluricanonical maps $|mK_X|$ for $
m \\geq r_n$. In joint work with Burt Totaro and Chengxi Wang (see https:
//arxiv.org/abs/2109.13383)\, we show that the constants $r_n$ grow at lea
st doubly exponentially. Conjecturally\, it's expected that the optimal b
ound is in fact doubly exponential. We do this by finding weighted projec
tive hypersurfaces of general type with extreme behavior: this includes ex
amples of very small volume and many vanishing plurigenera. We also consi
der the analogous questions for other classes of varieties and provide som
e conjecturally optimal examples. For instance\, we conjecture the termin
al Fano variety of minimal volume and the canonical Calabi-Yau variety of
minimal volume in each dimension.\n\nThe synchronous discussion for Louis
Esserâ€™s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2021-12-03-le (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/71/
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