Asymptotic expansion of the Bergman kernel via semi-classical symbolic calculus
by Yu-Chi Hou  

Vol. 17 No. 1 (2022) P.1~P.51

DOI:	https://doi.org/10.21915/BIMAS.2022101
	10.21915/BIMAS.2022101

ABSTRACT

We give a new proof on the pointwise asymptotic expansion for Bergman kernel associated to k-th tensor power of a hermitian holomorphic line bundle on the points where the curvature of the line bundle is positive and satisfies local spectral gap condition. The main point is to introduce a suitable semi-classical symbol space and related symbolic calculus inspired from recent work of Hsiao and Savale. Particularly, we establish the existence of pointwise asymptotic expansion on the positive part for certain semi-positive line bundles.

KEYWORDS
Bergman kernel, semi-classical symbol space

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32L10

MILESTONES

Received: 2022-02-20
Revised :
Accepted: 2022-03-20

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