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DTSTART;TZID=Asia/Seoul:20211111T160000
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SUMMARY:Jihun Yum\, Limits of Bergman kernels on a Tower of Coverings of Compact Kähler Manifolds
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe Bergman kernel BX\, which is by the definition the reproducing kernel of the space of L2 holomorphic n-forms on a n-dimensional complex manifold X\, is one of the important objects in complex geometry. In this talk\, we observe the asymptotics of the Bergman kernels\, as well as the Bergman metric\, on a tower of coverings. More precisely\, we show that\, for a tower of finite Galois coverings {ϕj : Xj → X} of compact Kähler manifold X converging to an infinite Galois covering ϕ : X~ → X\, the sequence of push-forward Bergman kernels ϕj*BXj locally uniformly converges to ϕ*BX~. Also\, we show that if the canonical line bundle KX~ of X~ is very ample\, then the canonical line bundle KXj of Xj is also very ample for sufficiently large j. This is a joint work with S. Yoo in IBS-CCG.
URL:https://ccg.ibs.re.kr/event/2021-11-11/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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