Equivariant Kodaira embedding of CR manifolds with circle action

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-Szegő 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.

arXiv comment40 pages. Corollary 1.6 in the first version is not correct. In this version, we corrected this mistake and added some references. arXiv admin note: text overlap with arXiv:1401.6647