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Communications in Algebra Volume 42, 2014 - Issue 11
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Original Articles

Kodaira Type Vanishing Theorem for the Hirokado Variety

Yukihide Takayama Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, JapanCorrespondence[email protected]
Pages 4744-4750 | Received 18 May 2012, Published online: 23 May 2014
 
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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.

2010 Mathematics Subject Classification:

Notes

Communicated by L. Ein.

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