Fubini-Study forms on punctured Riemann surfaces

2025/06/06 by Apredoaei, Razvan, Ma, Xiaonan, Wang, Lei
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.05863

Abstract

In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré 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 Poincaré 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].

Citations

• Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products
• Quotient of Bergman kernels on punctured Riemann surfaces
• Uniform sup-norm bounds on average for cusp forms of higher weights
• Extremal metrics and K-stability (PhD thesis)
• On the asymptotic expansion of Bergman kernel
• Szego kernels and a theorem of Tian

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