On complex vector bundles on rational threefolds

Abstract

It is known [14] that every topological complex vector bundle on a smooth rational surface admits an algebraic structure. In [10] one constructs algebraic vector bundles of rank 2 on with arbitrary Chern classes c1, c2 subject to the necessary topological condition c1 c2 = 0 (mod 2). However, in dimensions greater than 2 the Chern classes don't determine the topological type of a vector bundle. In [2] one classifies the topological complex vector bundles of rank 2 on and one proves that any such bundle admits an algebraic structure.