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Small Resolutions and Non-Liftable Calabi-Yau Threefolds

Slawomir Cynk, Duco van Straten

Number 9
Author Duco van Straten
Project C04
Year 2008

We use properties of small resolutions of the ordinary double point in dimension three to construct smooth non-liftable Calabi-Yau threefolds. In particular, we construct a smooth projective Calabi-Yau threefold over F3 that does not lift to characteristic zero and smooth projective Calabi-Yau threefold over F5 having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over Fp that do not lift to algebraic spaces in characteristic zero.

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