Abstract Bergman kernel expansion and its applications

Abstract

We give a purely complex geometric proof of the existence of the Bergman kernel expansion. Our method provides a sharper estimate, and in the case that the metrics are real analytic, we prove that the remainder decays faster than any polynomial.

Revised version of the previous version

References in corpus (1)

• A closed formula for the asymptotic expansion of the Bergman kernel

Cited by in corpus (3)

• Asymptotic expansion of polyanalytic Bergman kernels
• Sharp asymptotics for Toeplitz determinants, fluctuations and the gaussian free field on a Riemann surface
• Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds