Bergman Kernels of the Cheng-Yau metrics on quasi-projective manifolds

TL;DR

This paper investigates the asymptotic behavior of Bergman kernels associated with Cheng-Yau metrics on quasi-projective manifolds, revealing a quantum phenomenon near the divisor at infinity.

Contribution

It provides new asymptotic formulas for Bergman kernels near the divisor at infinity, highlighting quantum effects in this geometric setting.

Findings

Asymptotic behavior of Bergman kernels near the divisor at infinity

Identification of a quantum phenomenon close to the divisor

New formulas for Bergman kernel asymptotics in this context

Abstract

We show the asymptotics of the Bergman kernel function near the smooth divisor at infinity of the Cheng-Yau metric on quasi-projective manifolds. In particular, we show that there is a quantum phenomenon for the points very close to the divisor at infinity.