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Jihun Yum, Limits of Bergman kernels on a Tower of Coverings of Compact Kähler Manifolds

November 11, 2021 @ 4:00 pm - 5:00 pm KST

B266, IBS Korea, Republic of

     Speaker

Jihun Yum
IBS, Center for Complex Geometry

The 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 : XjX} 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.

Details

Date:
November 11, 2021
Time:
4:00 pm - 5:00 pm KST
Event Category:
Event Tags:

Venue

B266
IBS Korea, Republic of

Organizer

Sungyeon Kim
IBS 복소기하학연구단 Center for Complex Geometry
기초과학연구원 복소기하학연구단
대전 유성구 엑스포로 55 (우) 34126
IBS Center for Complex Geometry
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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