Bergman kernels on punctured Riemann surfaces

Abstract

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

42 pages, 2 figures; v.2 is a final update to agree with the published paper

References in corpus (3)

• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Extremal metrics and K-stability (PhD thesis)
• On the asymptotic behavior of Bergman kernels for positive line bundles

Cited by in corpus (5)

• Projective embedding of log Riemann surfaces and K-stability
• Analytic torsion for surfaces with cusps I. Compact perturbation theorem and anomaly formula
• Approximation of Regular Sasakian Manifolds
• Fubini-Study forms on punctured Riemann surfaces
• Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces