Exponential estimate for the asymptotics of Bergman kernels

By Xiaonan Ma, G. Marinescu. Mathematische Annalen, 2013

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We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. Further, we give Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line bundles.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a72f1ac19d80e412243f965cf1babbd8449802cf