Vanishing Theorems on Toric Varieties

Details Vanishing Theorems on Toric Varieties Vanishing Theorems on Toric Varieties

2000-01-25

arxiv.org/abs/math/0001142v3

Toho ku Math. J.(2) 54 (2002), 451--470.

Mathematics

Algebraic Geometry

21 pages. Revised version, to appear in Tohoku Mathematical Journal

Scientific paper

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.

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