Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity. (English) Zbl 07923288
Summary: 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 M. Jonsson and M. Mustaţă [Ann. Inst. Fourier 62, No. 6, 2145–2209 (2012; Zbl 1272.14016); J. Inst. Math. Jussieu 13, No. 1, 119–144 (2014; Zbl 1314.32047)]
and the effectiveness result of strong openness property of the modules at boundary points.
MSC:
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 32D15 | Continuation of analytic objects in several complex variables |
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