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Some Calabi–Yau threefolds with obstructed deformations over the Witt vectors

Published online by Cambridge University Press:  15 October 2004

Stefan Schröer
Stefan Schröer
Affiliation:
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germanystefan.schroeer@uni-bayreuth.de
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Abstract

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Some smooth Calabi–Yau threefolds in characteristic two and three that do not lift to characteristic zero are constructed. These threefolds are pencils of supersingular K3-surfaces. The construction depends on Moret-Bailly's pencil of abelian surfaces and Katsura's analysis of generalized Kummer surfaces. The threefold in characteristic two turns out to be nonrigid.

Keywords

Calabi–Yau manifoldsupersingular K3-surfacegeneralized Kummer surface14J2814J3014J3214K10
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1579 - 1592
Copyright
Foundation Compositio Mathematica 2004