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arXiv · 1204.1622

Kodaira type vanishing theorem for the Hirokado variety

Yukihide Takayama
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Abstract

The Hirokado variety is a Calabi-Yau threefold in characteristic 3 that is not liftable either to characteristic~0 or the ring $W_2$ of the second Witt vectors. Although Deligne-Illusie-Raynaud type Kodaira vanishing cannot be applied, we show that $H^1(X, L^{-1})=0$, for an ample line bundle such that $L^3$ has a non-trivial global section, holds for this variety.

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Yukihide Takayama. 2012-04-07. Kodaira type vanishing theorem for the Hirokado variety. https://doi.org/10.1080/0092872.2013.823546

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