Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

Dan Coman; Wen Lu; Xiaonan Ma; George Marinescu

doi:10.1016/j.aim.2022.108854

Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

Dan Coman, Wen Lu, Xiaonan Ma, George Marinescu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Given a sequence of positive Hermitian holomorphic line bundles (L_p,h_p) on a Kähler manifold X, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of L_p, under a natural convergence assumption on the sequence of curvatures c₁(L_p,h_p). We then apply this to study the asymptotic distribution of common zeros of random sequences of m-tuples of sections of L_p as p→+∞.

Original language	English (US)
Article number	108854
Journal	Advances in Mathematics
Volume	414
DOIs	https://doi.org/10.1016/j.aim.2022.108854
State	Published - Feb 1 2023

Keywords

Approximation of currents by analytic sets
Bergman kernel
Non-integral Kähler metric
Zeros of random holomorphic sections

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2022.108854

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title = "Bergman kernels and equidistribution for sequences of line bundles on K{\"a}hler manifolds",

abstract = "Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on a K{\"a}hler manifold X, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of Lp, under a natural convergence assumption on the sequence of curvatures c1(Lp,hp). We then apply this to study the asymptotic distribution of common zeros of random sequences of m-tuples of sections of Lp as p→+∞.",

keywords = "Approximation of currents by analytic sets, Bergman kernel, Non-integral K{\"a}hler metric, Zeros of random holomorphic sections",

author = "Dan Coman and Wen Lu and Xiaonan Ma and George Marinescu",

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T1 - Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

AU - Coman, Dan

AU - Lu, Wen

AU - Ma, Xiaonan

AU - Marinescu, George

PY - 2023/2/1

Y1 - 2023/2/1

N2 - Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on a Kähler manifold X, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of Lp, under a natural convergence assumption on the sequence of curvatures c1(Lp,hp). We then apply this to study the asymptotic distribution of common zeros of random sequences of m-tuples of sections of Lp as p→+∞.

AB - Given a sequence of positive Hermitian holomorphic line bundles (Lp,hp) on a Kähler manifold X, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of Lp, under a natural convergence assumption on the sequence of curvatures c1(Lp,hp). We then apply this to study the asymptotic distribution of common zeros of random sequences of m-tuples of sections of Lp as p→+∞.

KW - Approximation of currents by analytic sets

KW - Bergman kernel

KW - Non-integral Kähler metric

KW - Zeros of random holomorphic sections

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VL - 414

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108854

ER -

Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

Abstract

Keywords

ASJC Scopus subject areas

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