我们主要研究如下三个关于 Bergman 核的基本问题：1. Bergman 核的参数依赖性；2. Bergman 核的 Lp 估计和非对角线估计；3. 复流形的一个覆盖塔上的 Bergman 核的渐近行为。通过对这些问题的研究，我们有望了解 (1) 加权 Bergman 核的参数依赖性和全纯函数以及多次调和函数奇点理论之间的内在联系；(2) Bergman 核的估计在实解析有界区域之间的双全纯映射 Holder 连续延拓问题、Bergman 正交投射的 Lp 映射性质、以及进一步开发 Monge-Ampere 算子的应用前景；(3) 覆盖塔上Bergman 核的渐近行为与其它几何不变量之间的联系，以及可能存在的在数论方面的应用。

We mainly focus on the following three basic problems on the Bergman kernel: 1. Parameter dependence of the Bergman kernel; 2. Lp estimates and off-diagonal estimates of the Bergman kernel; 3. Asymptotic behavior of the Bergman kernel. Through the study of these problems, we hope to find (1) the intrinsic relationship between parameter dependence of the Bergman kernel and the singularity theory of holomorphic functions and plurisubharmonic functions; (2) the role of Bergman kernel estimates in the study of Holder continuous extension problem of biholomorphic mappings between bounded domains with real-analytic boundaries, and further develop the application prospect of the Monge-Ampere operator; (3) the relationship between the asymptotic behavior of the Bergman kernel and other geometric invariants, and probable applications in Number Theory.