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Vanishing theorems on toric varieties in positive characteristic

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An Erratum to this article was published on 14 March 2015

Abstract

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, Mustaţǎ and Fujino to the case where concerned Weil divisors are not necessarily torus invariant.

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Acknowledgments

I would like to express my gratitude to Professors Luc Illusie and Osamu Fujino for useful comments. I am very grateful to the referee for giving many useful suggestions, which make this paper more readable.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Qihong Xie

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  1. Qihong Xie
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Correspondence to Qihong Xie.

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Dedicated to Professor Yujiro Kawamata for his sixtieth birthday.

This paper was partially supported by the National Natural Science Foundation of China (Grant No. 11231003 and 11271070), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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Xie, Q. Vanishing theorems on toric varieties in positive characteristic. Math. Z. 276, 191–202 (2014). https://doi.org/10.1007/s00209-013-1193-2

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