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arXiv · 2007.00234

Algebraicity of the Bergman Kernel

Peter Ebenfelt·Ming Xiao·Hang Xu
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Abstract

Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a counterexample in dimension three constructed in this paper. As a corollary of our main theorem, we prove, e.g., that a smoothly bounded strictly pseudoconvex domain G in $\mathbb{C}^2$ has rational Bergman kernel if and only if there is a rational biholomorphism from G to the 2-dimensional unit ball.

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Peter Ebenfelt, Ming Xiao, Hang Xu. 2020-07-01. Algebraicity of the Bergman Kernel. https://arxiv.org/abs/2007.00234

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