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Vanishing Theorems on Toric Varieties

Mircea Mustata
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Abstract

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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Mircea Mustata. 2001-05-24. Vanishing Theorems on Toric Varieties. https://arxiv.org/abs/math/0001142

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