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

Details Some Calabi-Yau threefolds with obstructed deformations over the Witt vectors Some Calabi-Yau threefolds with obstructed deformations over the Witt vectors

2003-02-06

arxiv.org/abs/math/0302064v2

Compos. Math. 140 (2004), no. 6, 1579--1592

Mathematics

Algebraic Geometry

16 pages, some proofs simplified, discriminants in Theorem 6.4 corrected

Scientific paper

I construct some smooth Calabi-Yau threefolds in characteristic two and three
that do not lift to characteristic zero. 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.

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