Bergman kernel asymptotics and a pure analytic proof of Kodaira embedding theorem

TL;DR

This paper reviews recent advances in Bergman kernel asymptotics and provides an analytic proof of the Kodaira embedding theorem using Bergman kernel techniques.

Contribution

It offers a new analytic proof of the Kodaira embedding theorem based on Bergman kernel asymptotics, complementing existing algebraic methods.

Findings

Asymptotic expansion formulas for Bergman kernels

A new analytic proof of the Kodaira embedding theorem

Connections between Bergman kernel behavior and embedding properties

Abstract

In this paper, we survey some recent results about the asymptotic expansion of Bergman kernel and we give a Bergman kernel proof of Kodaira embedding theorem.