Kodaira type vanishing theorem for the Hirokado variety
Abstract
The Hirokado variety is a Calabi-Yau threefold in characteristic 3 that is not liftable either to characteristic~0 or the ring W2 of the second Witt vectors. Although Deligne-Illusie-Raynaud type Kodaira vanishing cannot be applied, we show that H1(X, L-1)=0, for an ample line bundle such that L3 has a non-trivial global section, holds for this variety.
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