bundles

complex geometry

# Contents

## Definition

A complex vector bundle is a vector bundle with respect complex vector spaces.

A omplex vector bundle with complex 1-dimensional fibers is a complex line bundle.

## Properties

### Oka-Grauert principle

The Oka-Grauert principle states that for any Stein manifold $X$ the holomorphic and the topological classification of complex vector bundles on $X$ coincide. The original reference is (Grauert 58).

## References

• Emery Thomas, Complex structures on real vector bundles (JSTOR)

In the context of GAGA:

Revised on May 21, 2014 22:16:45 by Urs Schreiber (82.136.246.44)