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SUMMARY:Fujita-type conjectures and Seshadri constants
DTSTART:20191119T151500
DTEND:20191119T161500
DTSTAMP:20260510T025352Z
UID:bad87ed0fc44ac324932a82ab6f93145f06569a8177858fe7b4028d9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Takumi Murayama (Princeton University)\nLet X be a smooth proj
 ective variety of dimension n and let L be an ample divisor on X. In 1988\
 , Fujita conjectured that K+(n+1)L is globally generated and K+(n+2)L is v
 ery ample\, where K is the canonical divisor on X. To tackle this conjectu
 re\, Demailly introduced Seshadri constants\, which measure the local posi
 tivity of L at a point x in X. While examples of Miranda seemed to indicat
 e that Seshadri constants could not be used to prove Fujita's conjecture\,
  we present a new characteristic-free approach to Fujita's conjecture usin
 g Seshadri constants. Our technique recovers some known results toward Fuj
 ita's conjecture over the complex numbers\, and proves new results for com
 plex varieties with singularities. We also describe joint work with Yajnas
 eni Dutta and Mihai Fulger\, in which we use Seshadri constants to prove g
 eneric positivity of direct images of pluricanonical bundles.
LOCATION:GR A3 30 https://plan.epfl.ch/?room==GR%20A3%2030
STATUS:CONFIRMED
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