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arXiv · 1502.01642

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

Chin-Yu Hsiao·George Marinescu
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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.

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Chin-Yu Hsiao, George Marinescu. 2015-02-05. Szeg\H{o} kernel asymptotics and Kodaira embedding theorems of Levi-flat CR manifolds. https://doi.org/10.4310/mrl.2017.v24.n5.a5

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