Superconnection and family Bergman kernels

2006/07/18 by Xiaonan Ma, Ma, Xiaonan, Weiping Zhang +1 · 4 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/0607404

openalex publication_date 2006/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.

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• Uniform RC-positivity of direct image bundles
• Asymptotic expansion of the variation of the Quillen metric and its moment map interpretation
• Mean curvature of direct image bundles
• Bernstein-Markov measures and Toeplitz theory

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