Fubini-Study forms on punctured Riemann surfaces
Complex Variables
2025-06-17 v2 Differential Geometry
Abstract
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincar\'e metric near the punctures, and a holomorphic line bundle that polarizes the metric. We show that the quotient of the induced Fubini-Study forms by Kodaira maps of high tensor powers of the line bundle and the Poincar\'e form near the singularity grows polynomially uniformly on a neighborhood of the singularity as the tensor power tends to infinity, as an application of the method in [5].
Keywords
Cite
@article{arxiv.2506.05863,
title = {Fubini-Study forms on punctured Riemann surfaces},
author = {Razvan Apredoaei and Xiaonan Ma and Lei Wang},
journal= {arXiv preprint arXiv:2506.05863},
year = {2025}
}
Comments
14 pages. Metadata has been updated. Published in Comptes Rendus. Math\'ematique