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.
ASJC Scopus subject areas
- Geometry and Topology