Vanishing theorems on toric varieties in positive characteristic
Vanishing theorems on toric varieties in positive characteristic
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DOI：
10.1007/s00209-013-1193-2
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发表时间：
2013-06
影响因子：
0.8
通讯作者：
Qihong Xie
中科院分区：
文献类型：
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作者：
Qihong Xie
利用复曲面簇的相对Frobenius态射的可提升性和复曲面簇的强可提升性证明了正特征复曲面簇上对数对的Bott消失定理、Hodge到de Rham谱序列的退化以及Kawamata-Viehweg消失定理。这些结果推广了达尼洛夫，Buch-Schlosen-Lauritzen-Mehta，Mustagen-Schlosen和Fujino的结果到有关Weil因子不一定是环面不变的情形.
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.