Sommese Vanishing for non-compact manifolds
Abstract
Description
The Kodaira-Nakano Vanishing Theorem has been generalized to the relative setting by A. Sommese. We prove a version of this theorem for non-compact manifolds. As an apllication, we prove that the cohomology of a fiber of a symplectic contraction is trivial in odd degrees and pure Hodge-Tate in even degrees.
No changes. Replacement is done just to add comments, which are: the preprint is left intact for historical reasons (there are references to it in other papers); however, as H. Esnault and E. Viehweg kindly indicated to me, the main result is actually an easy corollary of an old result of theirs. The application to symplectic manifolds, which is new, is now a part of my paper math.AG/0310186
No changes. Replacement is done just to add comments, which are: the preprint is left intact for historical reasons (there are references to it in other papers); however, as H. Esnault and E. Viehweg kindly indicated to me, the main result is actually an easy corollary of an old result of theirs. The application to symplectic manifolds, which is new, is now a part of my paper math.AG/0310186