Vector Bundles on Certain Non-algebraic Surfaces

摘要

@@ It is well-known that every holomorphic vector bundle is filtrable on a projective algebraicmanifold, and any complex vector bundle E of rank 2 on a projective algebraic surface admits aholomorphic structure iff c1 (E) = c1 (L) for some holomorphic line bundle L. And this is not truefor the non-algebraic case.