Fiberwise Bergman kernels, vector bundles, and log-subharmonicity

2022/10/29 by Shijie Bao, Bao, Shijie, Qi’an Guan +1
Mathematics · #32A36 #32D15 #32L15 #32Q28 #32W05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2210.16601

openalex publication_date 2022/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider Bergman kernels related to modules at boundary points for singular hermitian metrics on holomorphic vector bundles, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted L² integrals on sublevel sets of plurisubharmonic functions, and reprove an effectiveness result of the strong openness property of the modules.

Related

• Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity II -- on Stein manifolds
• Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity
• Curvature of vector bundles and subharmonicity of Bergman kernels
• Boundary points, minimal L² integrals and concavity property V -- vector bundles
• Upper bounds for Bergman kernels associated to positive line bundles with smooth Hermitian metrics