complex geometry

Contents

Definition

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

A complex 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 February 15, 2016 09:13:48 by Urs Schreiber (86.187.48.25)