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On non-liftable Calabi-Yau threefolds
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abstract
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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Cited by 1 Pith paper
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Non-liftable varieties via etale cohomology rings
A finite-field variety whose Q_ℓ-cohomology ring has no rational form, giving a simply-connected non-liftable example via a new cohomological obstruction.
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