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SUMMARY:Louis Esser (UCLA)
DTSTART:20211203T200000Z
DTEND:20211203T210000Z
DTSTAMP:20260407T214246Z
UID:agstanford/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/7
 1/">Varieties of general type with doubly exponential asymptotics</a>\nby 
 Louis Esser (UCLA) as part of Stanford algebraic geometry seminar\n\n\nAbs
 tract\nBy a theorem of Hacon–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 
 Esser’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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