A closed formula for the asymptotic expansion of the Bergman kernel
Differential Geometry
2013-03-28 v3 Mathematical Physics
math.MP
Abstract
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formula due to M. Englis and A. Loi.
Keywords
Cite
@article{arxiv.1103.3060,
title = {A closed formula for the asymptotic expansion of the Bergman kernel},
author = {Hao Xu},
journal= {arXiv preprint arXiv:1103.3060},
year = {2013}
}
Comments
25 pages, final version, Comm. Math. Phys