Modules at Boundary Points, Fiberwise Bergman Kernels, and Log-Subharmonicity

Abstract

In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which implies a concavity property related to the Bergman kernels. As applications, we reprove the sharp effectiveness result related to a conjecture posed by Jonsson–Mustaţă and the effectiveness result of strong openness property of the modules at boundary points.