On non-liftable Calabi-Yau threefolds

Abstract

Only two ways to construct non-liftable Calabi-Yau threefolds are currently known, one example by Hirokado and one method of Schröer. 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 Schröer, is introduced and the same calculations are performed for it.

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

Cited by in corpus (5)

• Twistor spaces for supersingular K3 surfaces
• Birational geometry of compactifications of Drinfeld half-spaces over a finite field
• Non-liftable Calabi-Yau varieties in characteristic $p\ge 5$
• Calabi-Yau threefolds over finite fields and torsion in cohomologies
• Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic $p>0$ and log weak Lefschetz conjecture for log crystalline cohomologies