Interface asymptotics of partial bergman kernels on S1-symmetric Kähler manifolds

Steve Zelditch, Peng Zhou

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

This article is concerned with asymptotics of equivariant Bergman kernels and partial Bergman kernels for polarized projective Kähler manifolds invariant under a Hamiltonian holomorphic S1 action. Asymptotics of partial Bergman kernel are obtained in the allowed region A resp. forbidden region F, generalizing results of Shiffman-Zelditch, Shiffman-Tate-Zelditch and Pokorny-Singer for toric Kähler manifolds. The main result gives scaling asymptotics of equivariant Bergman kernels and partial Bergman kernels in the transition region around the interface ∂A, generalizing recent work of Ross-Singer on partial Bergman kernels, and refining the Ross-Singer transition asymptotics to apply to equivariant Bergman kernels.

Original languageEnglish (US)
Pages (from-to)793-856
Number of pages64
JournalJournal of Symplectic Geometry
Volume17
Issue number3
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • Geometry and Topology

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