Bergman kernels on punctured Riemann surfaces
Differential Geometry
2021-04-08 v2 Complex Variables
Number Theory
Abstract
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric which equals the Poincar\'e metric near the punctures and a holomorphic line bundle which polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincar\'e metric. As a consequence, we obtain an optimal uniform estimate of the supremum norm of the Bergman kernel, involving a fractional growth order of the tensor power.
Keywords
Cite
@article{arxiv.1604.06337,
title = {Bergman kernels on punctured Riemann surfaces},
author = {Hugues Auvray and Xiaonan Ma and George Marinescu},
journal= {arXiv preprint arXiv:1604.06337},
year = {2021}
}
Comments
42 pages, 2 figures; v.2 is a final update to agree with the published paper