Arithmetic Moduli and Lifting of Enriques Surfaces

TL;DR

This paper constructs the moduli space of Enriques surfaces in positive characteristic, analyzes its structure, and demonstrates their lifting to characteristic zero, with key insights into their canonical double covers.

Contribution

It develops the moduli space of Enriques surfaces in positive characteristic and proves their liftability to characteristic zero, including in characteristic 2.

Findings

Moduli space of Enriques surfaces constructed in positive characteristic.

Enriques surfaces can be lifted to characteristic zero.

Canonical double cover is birational to a complete intersection of three quadrics in IP^5.

Abstract

We construct the moduli space of Enriques surfaces in positive characteristic and eventually over the integers, and determine its local and global structure. As an application, we show lifting of Enriques surfaces to characteristic zero. The key observation is that the canonical double cover of an Enriques surface is birational to the complete intersection of three quadrics in IP^5, even in characteristic 2.