Holomorphic vector bundles on non-algebraic surfaces

Andrei Teleman , Matei Toma

The paper is published: C. R. Acad. Sci. Paris, 334 (2002), 1-6

MSC 2000

32L05 Holomorphic bundles and generalizations

32J15 Compact surfaces

Abstract
The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is in general still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces.