Holomorphic vector bundles on non-algebraic surfaces
Algebraic Geometry
2007-05-23 v1 Complex Variables
Differential Geometry
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.
Cite
@article{arxiv.math/0201236,
title = {Holomorphic vector bundles on non-algebraic surfaces},
author = {Andrei Teleman and Matei Toma},
journal= {arXiv preprint arXiv:math/0201236},
year = {2007}
}
Comments
LaTeX, 6 pages, to appear in Comptes Rendus