Topic summary
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 : E → X 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.