manuscripta mathematica

, Volume 130, Issue 2, pp 233–249

Small resolutions and non-liftable Calabi-Yau threefolds


    • Instytut MatematykiUniwersytetu Jagiellońskiego
    • Institute of Mathematics of the Polish Academy of Sciences
  • Duco van Straten
    • Fachbereich 08, AG Algebraische GeometrieJohannes Gutenberg-Universität

DOI: 10.1007/s00229-009-0293-0

Cite this article as:
Cynk, S. & van Straten, D. manuscripta math. (2009) 130: 233. doi:10.1007/s00229-009-0293-0


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 14J32Secondary 14B1214J17

Copyright information

© Springer-Verlag 2009