Restricted Bergman kernel asymptotics

TL;DR

This paper studies a specialized form of Bergman kernels associated with high powers of line bundles on projective varieties, revealing their geometric significance and deriving integral formulas for restricted volume.

Contribution

It introduces a restricted Bergman kernel framework, clarifies the geometric interpretation of its leading term, and provides new integral representations for restricted volume.

Findings

Identified the geometric meaning of the leading term of the restricted Bergman kernel.

Derived integral representations for the restricted volume.

Enhanced understanding of the asymptotic behavior of restricted Bergman kernels.

Abstract

In this paper, we investigate a restricted version of Bergman kernels for high powers of a big line bundle over a smooth projective variety. The geometric meaning of the leading term is specified. As a byproduct, we derive some integral representations for the restricted volume.