Speaker : 蕭欽玉(Chin-Yu Hsiao)(本所)
Title : Szego kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds
Time : 2014-03-28 (Fri) 10:30 - 12:00
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: In this talk, I will report my recent work(arXiv:1401.6647). Let be the -th power of a CR line bundle over a CR manifold . Give , let be the Kohn Laplacian for forms with values in . We show that a certain microlocal conjugation of the spectral function of admits an asymptotic expansion in and we show further that the associated Szego kernel admits a full asymptotic expansion in if 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 actions.