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.

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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

Published 29 December 2017