A closed formula for the asymptotic expansion of the Bergman kernel

Details A closed formula for the asymptotic expansion of the Bergman kernel A closed formula for the asymptotic expansion of the Bergman kernel

2011-03-15

arxiv.org/abs/1103.3060v2

Mathematics

Differential Geometry

23 pages, slightly revised submitted version

Scientific paper

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 adjacency matrix 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.

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