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

Steve Zelditch, Peng Zhou

Research output: Contribution to journalArticle

2 Citations (Scopus)

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
StatePublished - Jan 1 2019

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Bergman Kernel
Partial
Equivariant
Invariant Manifolds
Scaling

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

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Interface asymptotics of partial bergman kernels on S1-symmetric Kähler manifolds. / Zelditch, Steve; Zhou, Peng.

In: Journal of Symplectic Geometry, Vol. 17, No. 3, 01.01.2019, p. 793-856.

Research output: Contribution to journalArticle

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