Approximation and equidistribution results for pseudo-effective line bundles

Dan Coman; George Marinescu; Viêt Anh Nguyên

doi:10.1016/j.matpur.2017.09.010

Approximation and equidistribution results for pseudo-effective line bundles

Dan Coman, George Marinescu, Viêt Anh Nguyên

Department of Mathematics

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

4 Scopus citations

Abstract

We study the distribution of the common zero sets of m-tuples of holomorphic sections of powers of m singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.

Original language	English (US)
Pages (from-to)	218-236
Number of pages	19
Journal	Journal des Mathematiques Pures et Appliquees
Volume	115
DOIs	https://doi.org/10.1016/j.matpur.2017.09.010
State	Published - Jul 2018

Keywords

Analytic cycle
Bergman kernel function
Fubini–Study current
Positive closed current
Pseudo-effective line bundle
Zeros of random holomorphic sections

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2017.09.010

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title = "Approximation and equidistribution results for pseudo-effective line bundles",

abstract = "We study the distribution of the common zero sets of m-tuples of holomorphic sections of powers of m singular Hermitian pseudo-effective line bundles on a compact K{\"a}hler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.",

keywords = "Analytic cycle, Bergman kernel function, Fubini–Study current, Positive closed current, Pseudo-effective line bundle, Zeros of random holomorphic sections",

author = "Dan Coman and George Marinescu and Nguy{\^e}n, {Vi{\^e}t Anh}",

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AU - Coman, Dan

AU - Marinescu, George

AU - Nguyên, Viêt Anh

PY - 2018/7

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N2 - We study the distribution of the common zero sets of m-tuples of holomorphic sections of powers of m singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.

AB - We study the distribution of the common zero sets of m-tuples of holomorphic sections of powers of m singular Hermitian pseudo-effective line bundles on a compact Kähler manifold. As an application, we obtain sufficient conditions which ensure that the wedge product of the curvature currents of these line bundles can be approximated by analytic cycles.

KW - Analytic cycle

KW - Bergman kernel function

KW - Fubini–Study current

KW - Positive closed current

KW - Pseudo-effective line bundle

KW - Zeros of random holomorphic sections

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Approximation and equidistribution results for pseudo-effective line bundles

Abstract

Keywords

ASJC Scopus subject areas

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