Abstract
We use Cox's description for sheaves on toric varieties and results about local cohomology with respect to monomial ideals to give a characteristic-free approach to vanishing results on toric varieties. As an application, we give a proof of a strong version 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.
Citation
Mircea Mustaţă. "Vanishing theorems on toric varieties." Tohoku Math. J. (2) 54 (3) 451 - 470, 2002. https://doi.org/10.2748/tmj/1113247605
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