# Kodaira vanishing theorem

From Diffgeom

*This is a vanishing theorem*

## Contents

## Statement

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`