Equivariant Kodaira embedding of CR manifolds with circle action

TL;DR

This paper proves an equivariant Kodaira embedding theorem for compact CR manifolds with circle actions by analyzing the asymptotic expansion of a weighted Fourier-Szegő kernel, advancing the understanding of CR geometry and embeddings.

Contribution

It introduces an equivariant Kodaira embedding theorem for CR manifolds with circle actions, based on asymptotic analysis of Fourier-Szegő kernels.

Findings

Asymptotic expansion of weighted Fourier-Szegő kernel established.

Equivariant Kodaira embedding theorem proven for CR manifolds with circle actions.

Provides new tools for embedding CR manifolds with symmetry.

Abstract

We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szeg\H{o} kernel of the CR sections in the high tensor powers admits a full asymptotic expansion. As a consequence, we establish an equivariant Kodaira embedding theorem.