Small resolutions and non-liftable Calabi-Yau threefolds

Small resolutions and non-liftable Calabi-Yau threefolds

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 that does not lift to characteristic zero and a smooth projective Calabi-Yau threef...

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Veröffentlicht in:Manuscripta mathematica 2009-10, Vol.130 (2), p.233-249
Hauptverfasser: Cynk, Sławomir, van Straten, Duco
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Zusammenfassung: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 that does not lift to characteristic zero and a smooth projective Calabi-Yau threefold over having an obstructed deformation. We also construct many examples of smooth Calabi-Yau algebraic spaces over that do not lift to algebraic spaces in characteristic zero.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-009-0293-0