Une classe de fibrés vectoriels holomorphes sur les 2-tores complexes. (A class of holomorphic vector bundles on two-dimensional complex tori). (French) Zbl 0711.32013
Let X be a compact complex surface and E a rank r topological vector bundle on S. Set \(2r^ 2(\Delta (E)):=2rc_ 2(E)-(r-1)c_ 1(E)^ 2.\) Here the author announces that if X is a complex 2-dimensional torus every topological vector bundle on X with \(c_ 1(E)\in NS(X)\) and \(\Delta(E)=0\) has a holomorphic structure. As a corollary, he obtains the existence of holomorphic vector bundles, E, on suitable non-algebraic 2- dimensional tori such that there is no coherent subsheaf F of E with \(0<rank(F)<rank(E)\).
Reviewer: E.Ballico
MSC:
| 32L05 | Holomorphic bundles and generalizations |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 32J15 | Compact complex surfaces |
| 32M05 | Complex Lie groups, group actions on complex spaces |
