Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces

TL;DR

This paper investigates the asymptotic behavior of the Bergman kernel near punctures on singular metrics over Riemann surfaces, with implications for quantum Hall effect density profiles.

Contribution

It provides new asymptotic analysis of Bergman kernels in singular settings, linking complex geometry with quantum physics phenomena.

Findings

Asymptotic profile of the Bergman kernel near punctures

Connection to density of states in quantum Hall effect

Insights into singular metric behavior on Riemann surfaces

Abstract

We consider singular metrics on a punctured Riemann surface and on a line bundle and study the behavior of the Bergman kernel in the neighbourhood of the punctures. The results have an interpretation in terms of the asymptotic profile of the density of states function of the lowest Landau level in quantum Hall effect.