Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann–Fock Model

Hamid Hezari, Casey Kelleher, Shoo Seto, Hang Xu

Research output: Contribution to journalArticle

Abstract

We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated with the kth tensor powers of a positive line bundle L in a 1k-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential kφ in a 1k-neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann–Fock metric. We then prove that the Bergman kernel is also an asymptotic perturbation of the Bargmann–Fock Bergman kernel.

Original languageEnglish (US)
Pages (from-to)2602-2638
Number of pages37
JournalJournal of Geometric Analysis
Volume26
Issue number4
DOIs
StatePublished - Oct 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Asymptotic expansion
  • Bargmann–Fock space
  • Bergman kernel
  • Kahler manifolds

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