Topic summary

Holomorphic line bundle

Holomorphic line bundle

Extracted from the Wikipedia article Holomorphic vector bundle.

In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifoldX such that the total space E is a complex manifold and the projection mapπ : EX is holomorphic. Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle. A holomorphic line bundle is a rank one holomorphic vector bundle.