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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