Moduli and periods of simply connected Enriques surfaces

Abstract

We describe a period map for those simply connected Enriques surfaces in characteristic 2 whose canonical double cover is K3. The moduli stack for these surfaces has a Deligne-Mumford quotient that is an open substack of a ${\mathbb{P}}^1$-bundle over the period space. We also give some general results relating local and global moduli for algebraic varieties and describe the difference in their dimensions in terms of the failure of the automorphism group scheme to be reduced.

References in corpus (1)

• On exceptional Enriques surfaces

Cited by in corpus (8)

• Infinitesimal automorphisms of algebraic varieties and vector fields on elliptic surfaces
• A 1-dimensional family of Enriques surfaces in characteristic 2 covered by the supersingular K3 surface with Artin invariant 1
• Weyl group covers for Brieskorn's resolutions in all characteristics and the integral cohomology of $G/P$
• Cycle classes on the moduli of K3 surfaces in positive characteristic
• Automorphisms of unnodal Enriques surfaces
• A note on stable sheaves on Enriques surfaces II
• Vanishing of Brauer groups of moduli stacks of stable curves
• The moduli space of marked supersingular Enriques surfaces