Algebraicity of the Bergman kernel
Algebraicity of the Bergman kernel
复制标题
Bergman 核的代数性
DOI：
10.1007/s00208-023-02720-9
复制
发表时间：
2020
影响因子：
1.4
通讯作者：
Hangjun Xu
中科院分区：
文献类型：
--
作者：
P. Ebenfelt;Ming Xiao;Hangjun Xu
我们的主要结果介绍了一种新的方法来表征二维有限球代数的Bergman核的代数。这个特征是特定的二维和失败的高维，如本文所示的反例在三维构造。作为我们的主要定理的推论，我们证明，例如，证明了光滑有界严格伪凸Domain G_n具有有理Bergman核当且仅当存在从G_n到G_n的有理双全纯.
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 domainGinhas rational Bergman kernel if and only if there is a rational biholomorphism fromGto.