Approximation and equidistribution results for pseudo-effective line bundles

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 thes...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2018-07, Vol.115, p.218-236
Main Authors: Coman, Dan, Marinescu, George, Nguyên, Viêt-Anh
Format: Article
Language:English
Subjects:
Analytic cycle
Bergman kernel function
Fubini–Study current
Mathematics
Positive closed current
Pseudo-effective line bundle
Zeros of random holomorphic sections
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Summary: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. Nous étudions la distribution de l'ensemble des zéros communs de m-tuplets de sections holomorphes de puissances de m fibrés en droites hermitiens singuliers pseudo-effectifs sur une variété kählérienne compacte. Comme application, nous obtenons des conditions suffisantes pour que le produt extérieur des courants de courbure de ces fibrés puisse être approché par des cycles analytiques.
ISSN:0021-7824
DOI:10.1016/j.matpur.2017.09.010