Every compact complex manifold admits a non-trivial holomorphic vector bundle.

Jörg Winkelmann

Appeared in:

Rev. Roumaine Math. Pures Appl. 38 743--744 (1993)


Abstract.

We prove that every positive-dimensional compact complex manifold admits a non-trivial holomorphic vector bundle. This answers a question of Banica.


Addendum

A later result (which is contained in my Habilitationsschrift) implies that this non-trivial holomorphic vector bundle can be choosen in such a way that its rank does not exceed the dimension of the manifold.
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