Mathematical Research Letters

Volume 24 (2017)

Number 5

Szegő kernel asymptotics and Kodaira embedding theorems of Levi-flat CR manifolds

Pages: 1385 – 1451



Chin-Yu Hsiao (Institute of Mathematics, Academia Sinica and National Center for Theoretical Sciences, Taipei, Taiwan)

George Marinescu (Mathematisches Institut, Universität zu Köln, Germany; and Institute of Mathematics, Romanian Academy, Bucharest, Romania)


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 Szegő kernel admits an asymptotic expansion with respect to high powers of $L$. As an application, we give a Szegő kernel proof of the Kodaira type embedding theorem on Levi-flat CR manifolds due to Ohsawa and Sibony.

The first-named author was partially supported by Taiwan Ministry of Science of Technology project 103-2115-M-001-001, 104-2628-M-001-003-MY2 and the Golden-Jade fellowship of Kenda Foundation. The secondnamed author was partially supported by the DFG project SFB TRR 191 and Université Paris 7.

Received 22 February 2015

Accepted 27 January 2017

Published 29 December 2017