Construction of boundary invariants and the logarithmic singularity of the Bergman kernel

2000/10/02 by Kengo Hirachi · 1 citation
Mathematics · #math.CV #msc:32Axx #msc:46Exx #msc:46N20

paper · pdf

published as Ann. of Math. (2) 151 (2000), no. 1, 151--191 · 41 pages

arxiv created 2000/10/02 · arxiv updated 2009/11/30

Abstract

This paper studies Fefferman's program \citeF3 of expressing the singularity of the Bergman kernel, for smoothly bounded strictly pseudoconvex domains Ω⊂\Cⁿ, in terms of local biholomorphic invariants of the boundary. By \citeF1, the Bergman kernel on the diagonal K(z,cz) is written in the form K=ϕr^-n-1+ψlog r \qtextwith ϕ,ψ∈ C^∞(\cΩ), where r is a (smooth) defining function of Ω. Recently, Bailey, Eastwood and Graham \citeBEG, building on Fefferman's earlier work \citeF3, obtained a full invariant expression of the strong singularity ϕr^-n-1. The purpose of this paper is to give a full invariant expression of the weak singularity ψlog r.

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• Bergman kernels over polarized Kähler manifolds, Bergman logarithmic flatness, and a question of Lu-Tian

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