A holomorphic vector bundle is a complex vector bundle 
over a complex manifold whose total
space 
is a complex manifold, whose projection 
and local trivializations are holomorphic
maps, and whose transition functions are
holomorphic maps. The fibers 
are copies of 
, and the transition
functions act linearly on them. The
simplest example is a holomorphic line bundle,
where each fiber is a copy of 
.
Holomorphic Vector Bundle
See also
Complex Manifold, Hermitian Metric, Holomorphic Function, Holomorphic Line Bundle, Holomorphic Tangent Bundle, Vector BundlePortions of this entry contributed by Todd Rowland
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Holomorphic Vector Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolomorphicVectorBundle.html