nLab
complex vector bundle

Contents

Context

Bundles

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 XX the holomorphic and the topological classification of complex vector bundles on XX coincide. The original reference is (Grauert 58).

Relation to holomorphic vector bundles

See at Koszul-Malgrange theorem.

References

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

In the context of GAGA:

Last revised on November 25, 2020 at 05:11:13. See the history of this page for a list of all contributions to it.