Vanishing Theorems on Toric Varieties in Positive Characteristic

Details Vanishing Theorems on Toric Varieties in Positive Characteristic Vanishing Theorems on Toric Varieties in Positive Characteristic

2010-10-27

arxiv.org/abs/1010.5580v2

Mathematics

Algebraic Geometry

13 pages

Scientific paper

We use the liftability of the relative Frobenius morphism of toric varieties and the strong liftability of toric varieties to prove the Bott vanishing theorem, the degeneration of the Hodge to de Rham spectral sequence and the Kawamata-Viehweg vanishing theorem for log pairs on toric varieties in positive characteristic. These results generalize those results of Danilov, Buch-Thomsen-Lauritzen-Mehta, Musta\c{t}\v{a} and Fujino to the case where concerned Weil divisors are not necessarily torus invariant.

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