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...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.展开更多
基金Foundation item:Supported by NSFC(No.10071051)NSF of Beijing(No.1002004)Outslsanding Youth Foundation of NNSFC(Grant No.19825102)
文摘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.