Szeg\H{o} kernel asymptotics and Kodaira embedding theorems of Levi-flat CR manifolds

TL;DR

This paper establishes asymptotic expansions for Szeg\

Contribution

It provides a Szeg\

Findings

Asymptotic expansion of Szeg\

Proof of Kodaira embedding theorem for Levi-flat CR manifolds

Microlocal conjugation techniques for Szeg\

Abstract

Let $X$ be an orientable compact Levi-flat CR manifold and let $L$ be a positive CR complex line bundle over $X$. We prove that certain microlocal conjugations of the associated Szeg\H{o} kernel admits an asymptotic expansion with respect to high powers of $L$. As an application, we give a Szeg\H{o} kernel proof of the Kodaira type embedding theorem on Levi-flat CR manifolds due to Ohsawa and Sibony.