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Exponential estimate for the asymptotics of Bergman kernels

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Abstract

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.

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Authors and Affiliations

  1. Institut Universitaire de France, Université Paris Diderot-Paris 7, UFR de Mathématiques, Case 7012, 75205, Paris Cedex 13, France

    Xiaonan Ma

  2. Universität Zu Köln, Mathematisches Institut, Weyertal 86-90, 50931, Cologne, Germany

    George Marinescu

  3. Institute of Mathematics ‘Simion Stoilow’, Romanian Academy, Bucharest, Romania

    George Marinescu

Authors
  1. Xiaonan Ma
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  2. George Marinescu
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Corresponding author

Correspondence to George Marinescu.

Additional information

X. Ma: Partially supported by Institut Universitaire de France and funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative.

G. Marinescu: Partially supported by DFG funded projects SFB/TR 12, MA 2469/2-1 and ENS Paris.

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Ma, X., Marinescu, G. Exponential estimate for the asymptotics of Bergman kernels. Math. Ann. 362, 1327–1347 (2015). https://doi.org/10.1007/s00208-014-1137-0

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  • DOI: https://doi.org/10.1007/s00208-014-1137-0

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