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Nadia SUSY
Nadia SUSY
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A vector bundle over a complex manifold is said to be holomorphic if its trivialization maps are biholomorphic maps. What is a "natural" example example of a vector bundle over compact complex manifold which is not holomorphic? I guess by "natural" I mean that one would be interested in such examples for reasons besides them being a counter example.

TO CLARIFY: I am interested in

i) COMPLEX VECTOR BUNDLES

ii) NOT ADMITTING ANY HOLOMORPHIC STRUCTURE

A vector bundle over a complex manifold is said to be holomorphic if its trivialization maps are biholomorphic maps. What is a "natural" example example of a vector bundle over compact complex manifold which is not holomorphic? I guess by "natural" I mean that one would be interested in such examples for reasons besides them being a counter example.

A vector bundle over a complex manifold is said to be holomorphic if its trivialization maps are biholomorphic maps. What is a "natural" example example of a vector bundle over compact complex manifold which is not holomorphic? I guess by "natural" I mean that one would be interested in such examples for reasons besides them being a counter example.

TO CLARIFY: I am interested in

i) COMPLEX VECTOR BUNDLES

ii) NOT ADMITTING ANY HOLOMORPHIC STRUCTURE

Source Link
Nadia SUSY
Nadia SUSY
  • 835
  • 6
  • 23

Vector bundle over compact complex manifold which is not holomorphic?

A vector bundle over a complex manifold is said to be holomorphic if its trivialization maps are biholomorphic maps. What is a "natural" example example of a vector bundle over compact complex manifold which is not holomorphic? I guess by "natural" I mean that one would be interested in such examples for reasons besides them being a counter example.