The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator

TL;DR

This paper computes the second coefficient in the asymptotic expansion of the Bergman kernel related to the Hodge-Dolbeault operator for high powers of a Hermitian line bundle with non-degenerate curvature, using formal power series methods.

Contribution

It provides a detailed calculation of the second coefficient in the asymptotic expansion, extending previous work on Bergman kernels and Hodge-Dolbeault operators.

Findings

Explicit formula for the second coefficient obtained

Method applied to non-degenerate curvature cases

Enhances understanding of Bergman kernel asymptotics

Abstract

We calculate the second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator associated to high powers of a Hermitian line bundle with non-degenerate curvature, using the method of formal power series developed by Ma and Marinescu.