Fubini-Study forms on punctured Riemann surfaces

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].

14 pages. Metadata has been updated. Published in Comptes Rendus. Mathématique

References in corpus (5)

• Generalized Bergman kernels on symplectic manifolds
• Bergman kernels on punctured Riemann surfaces
• Hilbert-Mumford criterion for nodal curves
• Semiclassical Ohsawa-Takegoshi extension theorem and asymptotics of the orthogonal Bergman kernel
• Estimates of Kähler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products