Kodaira type vanishing theorem for the Hirokado variety

Details Kodaira type vanishing theorem for the Hirokado variety Kodaira type vanishing theorem for the Hirokado variety

2012-04-07

arxiv.org/abs/1204.1622v1

Mathematics

Algebraic Geometry

6 pages

Scientific paper

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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