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

被引：2

作者：

Coman, Dan ^{[1
]}

Lu, Wen ^{[2
]}

Ma, Xiaonan ^{[3
]}

Marinescu, George ^{[4
,5
]}

机构：

[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[3] Univ Paris Cite, Batiment Sophie Germain, CNRS, IMJ,PRG,UFR Math,Case 7012, F-75205 Paris 13, France

[4] Univ Cologne, Dept Math & Comp Sci, Weyertal 86-90, D-50931 Cologne, Germany

[5] Romanian Acad, Inst Math Sim Stoilow, Bucharest, Romania

来源：

ADVANCES IN MATHEMATICS | 2023年 / 414卷

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

Bergman kernel; Non-integral K?hler metric; Zeros of random holomorphic; sections; Approximation of currents by; analytic sets; SINGULAR METRICS; ZEROS; APPROXIMATION; SECTIONS; THEOREM;

D O I：

10.1016/j.aim.2022.108854

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a sequence of positive Hermitian holomorphic line bun-dles (Lp, hp) on a Kahler manifold X, we establish the asymp-totic expansion of the Bergman kernel of the space of global holomorphic sections of Lp, under a natural convergence as-sumption 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 -> +infinity. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：34

共 37 条

[1]

[Anonymous], 1981, Ann. of Math. Stud.

[2]

[Anonymous], Complex analytic and differential geometry

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