Equivariant Kodaira Embedding for CR Manifolds with Circle Action

Abstract

We consider a compact CR manifold with a transversal CR locally free circle action endowed with an ${\mathit{S}}^1$-equivariant 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.