Bergman kernel and complex singularity exponent

Details Bergman kernel and complex singularity exponent Bergman kernel and complex singularity exponent

2009-11-21

arxiv.org/abs/0911.4169v1

Mathematics

Complex Variables

to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthday

Scientific paper

We give a precise estimate of the Bergman kernel for the model domain defined
by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where
$F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$,
in terms of the complex singularity exponent of $F$.

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