Moret-Bailly families and non-liftable schemes

Abstract

Generalizing the Moret-Bailly pencil of supersingular abelian surfaces to higher dimensions, we construct for each field of characteristic p>0 a smooth projective variety with trivial dualizing sheaf that does not formally lift to characteristic zero. Our approach heavily relies on local unipotent group schemes, the Beauville--Bogomolov Decomposition for Kähler manifolds with $c_1=0$, and equivariant deformation theory

31 pages, Theorem 5.1 extended to the case that ω_Y is anti-nef, results on non-existence of formal liftings corrected by adding assumptions, Section 9 on non-existence of liftings to rings of Witt vectors added

References in corpus (2)

• The weak Beauville--Bogomolov decomposition in characteristic $p\ge 0$
• Non-liftable Calabi-Yau varieties in characteristic $p\ge 5$

Cited by in corpus (1)

• The weak Beauville--Bogomolov decomposition in characteristic $p\ge 0$