Vol. 289, No. 1, 2017

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ISSN: 0030-8730
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 Lp 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
Authors
Tien-Cuong Dinh
Department of Mathematics
National University of Singapore
10 Lower Kent Ridge Road
Singapore 119076
Singapore
Xiaonan Ma
Institut de Mathématiques de Jussieu – Paris Rive Gauche
UFR de Mathématiques
Université Paris Diderot - Paris 7
Case 7012
75205 Paris Cedex 13
France
Viêt-Anh Nguyên
Laboratoire de Mathematiques Paul Painlevé
Université de Lille 1
CNRS UMR 8524
59655 Villeneuve d’Asq CEDEX
France