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Bergman kernel and complex singularity exponent

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Abstract

We give a precise estimate of the Bergman kernel for the model domain defined by Ω F = “(z,w) ∈ ℂn+1: Im w − |F(z)|2 > 0”, where F = (f 1, ..., f m ) is a holomorphic map from ℂn to ℂm, in terms of the complex singularity exponent of F.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    BoYong Chen

  2. Global Leadership School, Handong Global University, Pohang, 791-708, Korea

    HanJin Lee

Authors
  1. BoYong Chen
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  2. HanJin Lee
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Correspondence to BoYong Chen.

Additional information

Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

This work was supported by the New Century Excellent Talent Project (Grant No. NECT-05-0380), the Chinese Excellent Doctorate’s Degree Thesis (Grant No. 200519), Fok Ying Tung Education Fundation, and National Natural Science Foundation of China (Grant No. 10871145)

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Chen, B., Lee, H. Bergman kernel and complex singularity exponent. Sci. China Ser. A-Math. 52, 2590–2603 (2009). https://doi.org/10.1007/s11425-009-0033-7

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  • DOI: https://doi.org/10.1007/s11425-009-0033-7

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