Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds

Sungmin Yoo; Jihun Yum

doi:10.1007/s00208-022-02552-z

Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds

Sungmin Yoo
, Jihun Yum^*

^*Corresponding author for this work

Department of Mathematics Education

Incheon National University
Institute for Basic Science

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

Abstract

We prove the convergence of the Bergman kernels and the L²-Hodge numbers on a tower of Galois coverings {X_j} of a compact Kähler manifold X converging to an infinite Galois (not necessarily universal) covering (Formula Presented.). We also show that, as an application, sections of canonical line bundle KX_j for sufficiently large j give rise to an immersion into some projective space, if so do sections of (Formula Presented.).

Original language	English
Pages (from-to)	1609-1628
Number of pages	20
Journal	Mathematische Annalen
Volume	388
Issue number	2
DOIs	https://doi.org/10.1007/s00208-022-02552-z
State	Published - 2024.02

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title = "Limit of Bergman kernels on a tower of coverings of compact K{\"a}hler manifolds",

abstract = "We prove the convergence of the Bergman kernels and the L2-Hodge numbers on a tower of Galois coverings \{Xj\} of a compact K{\"a}hler manifold X converging to an infinite Galois (not necessarily universal) covering (Formula Presented.). We also show that, as an application, sections of canonical line bundle KXj for sufficiently large j give rise to an immersion into some projective space, if so do sections of (Formula Presented.).",

author = "Sungmin Yoo and Jihun Yum",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.",

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AU - Yoo, Sungmin

AU - Yum, Jihun

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.

PY - 2024/2

Y1 - 2024/2

N2 - We prove the convergence of the Bergman kernels and the L2-Hodge numbers on a tower of Galois coverings {Xj} of a compact Kähler manifold X converging to an infinite Galois (not necessarily universal) covering (Formula Presented.). We also show that, as an application, sections of canonical line bundle KXj for sufficiently large j give rise to an immersion into some projective space, if so do sections of (Formula Presented.).

AB - We prove the convergence of the Bergman kernels and the L2-Hodge numbers on a tower of Galois coverings {Xj} of a compact Kähler manifold X converging to an infinite Galois (not necessarily universal) covering (Formula Presented.). We also show that, as an application, sections of canonical line bundle KXj for sufficiently large j give rise to an immersion into some projective space, if so do sections of (Formula Presented.).

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Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds

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