报告摘要：
| Grauert and Riemenschneider conjectured that if a Hermitian line bundle over a compact complex manifold is semipositive everywhere and positive at a point then it is big. The conjecture was proved by Siu using the Dbar-method and Demailly using the Demailly's holomorphic Morse inequalities. In this talk, we will first recall the Classical Morse inequalities on differential manifolds and Demailly’s holomorphic Morse inequalities on complex manifolds. Then we will explain the Morse inequalities on CR manifolds with group actions. By using the Morse inequalities on CR manifolds we give a Gruaert-Riemenschneider criterion on CR manifolds which implies there are many CR sections of a positive CR line bundle. At last, we will talk about the Kodaira embedding theorems for CR manifolds with group actions.
|
