manuscripta mathematica

, Volume 130, Issue 2, pp 233–249

Small resolutions and non-liftable Calabi-Yau threefolds

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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 \({\mathbb{F}_3}\) that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over \({\mathbb{F}_5}\) having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over \({\mathbb{F}_p}\) that do not lift to algebraic spaces in characteristic zero.

Mathematics Subject Classification (2000)

Primary 14J32 Secondary 14B12 14J17 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Instytut MatematykiUniwersytetu JagiellońskiegoKrakówPoland
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland
  3. 3.Fachbereich 08, AG Algebraische GeometrieJohannes Gutenberg-UniversitätMainzGermany

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