Bergman kernels on punctured Riemann surfaces | Zendy

Hugues Auvray | Zendy; Xiaonan Ma | Zendy; George Marinescu | Zendy

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Bergman kernels on punctured Riemann surfaces

Author(s) -

Hugues Auvray,

Xiaonan Ma,

George Marinescu

Publication year - 2016

Publication title -

comptes rendus mathématique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.803

H-Index - 68

eISSN - 1778-3569

pISSN - 1631-073X

DOI - 10.1016/j.crma.2016.08.006

Subject(s) - mathematics , bergman kernel , holomorphic function , riemann surface , line bundle , pure mathematics , gravitational singularity , unit disk , mathematical analysis

In this paper, we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures and a holomorphic line bundle that polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincaré metric. As a consequence, we obtain an optimal uniform estimate of the supremum norm of the Bergman kernel function, involving a fractional growth order of the tensor power

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