2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126459I 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.16 pages, some proofs simplified, discriminants in Theorem 6.4 correctedAlgebraic Geometry14J28, 14J30, 14J32, 14K10text