Asian Journal of Mathematics

Volume 24 (2020)

Number 3

Equivariant asymptotics of Szegö kernels under Hamiltonian $SU(2)$-actions

Pages: 501 – 532

DOI: https://dx.doi.org/10.4310/AJM.2020.v24.n3.a6

Authors

Andrea Galasso (Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Milano, Italy; and National Taiwan University, Taipei, Taiwan)

Roberto Paoletti (Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Milano, Italy)

Abstract

Let $M$ be complex projective manifold, and $A$ a positive line bundle on it. Assume that $G = SU(2)$ acts on $M$ in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to $A$. Then there is an associated unitary representation of $G$ on the associated algebro-geometric Hardy space, and the isotypical components are all finite dimensional. We consider the local and global asymptotic properties of the equivariant projector associated to a weight $k \nu$, when $\nu$ is fixed and $k \to + \infty$.

Keywords

Hamiltonian action, Szegö kernel, Hardy space, equivariant asymptotics

2010 Mathematics Subject Classification

30H10, 32M05, 41A60, 53D20, 53D35, 53D50, 57S15

Full Text (PDF format)

Received 21 June 2018

Accepted 4 October 2019

Published 9 October 2020