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arXiv · 2506.05863

Fubini-Study forms on punctured Riemann surfaces

Razvan Apredoaei·Xiaonan Ma·Lei Wang
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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].

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Razvan Apredoaei, Xiaonan Ma, Lei Wang. 2025-06-06. Fubini-Study forms on punctured Riemann surfaces. https://doi.org/10.5802/crmath.763

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