On the asymptotic behavior of Bergman kernels for positive line bundles

Tien-Cuong Dinh, Xiaonan Ma and Viêt-Anh Nguyên

Vol. 289 (2017), No. 1, 71–89

DOI: 10.2140/pjm.2017.289.71

Abstract

Let $L$ be a positive line bundle on a projective complex manifold. We study the asymptotic behavior of Bergman kernels associated with the tensor powers $L^p$ of $L$ as $p$ tends to infinity. The emphasis is the dependence of the uniform estimates on the positivity of the Chern form of the metric on $L$. This situation appears naturally when we approximate a semipositive singular metric by smooth positively curved metrics.

Keywords

Bergman kernel, Dirac operator, Laplacian operator

Mathematical Subject Classification 2010

Primary: 32U15

Secondary: 32L05

Milestones

Received: 8 March 2016

Accepted: 10 October 2016

Published: 12 May 2017