On non-liftable Calabi-Yau threefolds

Details On non-liftable Calabi-Yau threefolds On non-liftable Calabi-Yau threefolds

2003-06-30

arxiv.org/abs/math/0306435v2

Mathematics

Algebraic Geometry

31 pages. An improper use of a result of Deligne and Illusie has been replaced with a proper one. Also some other minor correc

Scientific paper

Only two ways to construct non-liftable Calabi-Yau threefolds are currently known, one example by Hirokado and one method of Schr\"oer. This article computes some cohomological invariants of these examples of non-liftable Calabi-Yau threefolds, in particular it computes their mini-versal deformations. One conclusion is that their mixed characteristic mini-versal deformation spaces are actually smooth over the characteristic $p$ base field. Furthermore, a new family, constructed in the spirit of Schr\"oer, is introduced and the same calculations are performed for it.

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