Vanishing Theorems on Toric Varieties
Abstract
Description
We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary toric varieties. As an application, we give a proof of a strong form of Fujita's conjecture in the case of toric varieties. We also prove that every sheaf on a toric variety corresponds to a module over the homogeneous coordinate ring, generalizing Cox's result for the simplicial case.
21 pages. Revised version, to appear in Tohoku Mathematical Journal
21 pages. Revised version, to appear in Tohoku Mathematical Journal