Speaker : 蕭欽玉(Chin-Yu Hsiao)(本所) Szego kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds 2014-03-28 (Fri) 10:30 - 12:00 Seminar Room 617, Institute of Mathematics (NTU Campus) In this talk, I will report my recent work(arXiv:1401.6647). Let $L^k$ be the $k$-th power of a CR line bundle over a CR manifold $X$. Give $q$, let $[]^{(q)}_{b,k}$ be the Kohn Laplacian for $(0,q)$ forms with values in $L^k$. We show that a certain microlocal conjugation of the spectral function of $[]^{(q)}_{b,k}$ admits an asymptotic expansion in $k$ and we show further that the associated Szego kernel admits a full asymptotic expansion in $k$ if $[]^{(q)}_{b,k}$ has small spectral gap. By using these asymptotics, we establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR $S^1$ actions.