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

Abstract

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. © Foundation Compositio Mathematica 2004.