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SUMMARY:Yoshinori Hashimoto (Osaka Metropolitan Univ)
DTSTART:20230505T150000Z
DTEND:20230505T161500Z
DTSTAMP:20260423T005710Z
UID:CIRGET/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/99/">
 Uniform Hörmander estimates for flat nontrivial line bundles</a>\nby Yosh
 inori Hashimoto (Osaka Metropolitan Univ) as part of CRM - Séminaire du C
 IRGET / Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\n
 Hörmander’s $L^2$-estimates for the $\\bar{\\partial}$ operators on hol
 omorphic line bundles are of fundamental importance in complex analytic ge
 ometry\, whose conventional proof crucially relies on the positivity of th
 e line bundle. In this talk\, we prove the $L^2$-estimates for the solutio
 ns to the $\\bar{\\partial}$ equation that hold uniformly for all flat non
 trivial line bundles on compact Kähler manifolds\, whose main feature is 
 the quantitative description of the blow-up behaviour as the line bundle a
 pproaches the trivial one. A key ingredient in the proof is the observatio
 n that line bundles with vanishing first Chern classes are topologically t
 rivial and can be identified with the trivial bundle with the "perturbed" 
 $\\bar{\\partial}$ operator which we define in terms of coordinates on the
  Picard variety. This is a joint work with Takayuki Koike.\n
LOCATION:https://researchseminars.org/talk/CIRGET/99/
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