Kodaira vanishing theorem
This is a vanishing theorem
Let be a holomorphic line bundle on a compact Kahler manifold , whose topological Chern class can be represented by a closed -form which is positive definite. Let be any other holomorphic vector bundle. Then the cohomology groups vanish for large enough whenever is at least 1.
Relation with other results
Kodaira embedding theorem
Further information: Kodaira embedding theorem
Lichnerowicz vanishing theorem
Further information: Lichnerowicz vanishing theorem