Small Resolutions and Non-Liftable Calabi-Yau threefolds
Abstract
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 3 that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over 5 having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over p that do not lift to algebraic spaces in characteristic zero.
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