论文标题
伯格曼内核的代数
Algebraicity of the Bergman Kernel
论文作者
论文摘要
我们的主要结果引入了一种新的方式，可以通过其伯格曼内核代数来表征二维有限球商。这种特征是二维的特殊性，并且在较高的维度中失败，正如本文构建的维度第三的反例所示。作为我们的主要定理的推论，我们证明，例如，在$ \ mathbb {c}^2 $中，严格界限的pseudoconvex域g具有理性的伯格曼内核，并且只有在G到2维单个单位球中有合理的Biholomorphism。
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.
