On Enriques surfaces in characteristic 2 with a finite group of automorphisms

TL;DR

This paper classifies Enriques surfaces with finite automorphism groups in characteristic 2, identifying specific types and constructing a family with automorphism group S_5, expanding understanding in positive characteristic.

Contribution

It determines which types of Enriques surfaces with finite automorphism groups exist in characteristic 2 and constructs a family with automorphism group S_5.

Findings

Existence of classical and supersingular Enriques surfaces with automorphism group S_5 in characteristic 2

Classification of Enriques surfaces with finite automorphism groups in characteristic 2

Identification of seven types of such surfaces in the complex case

Abstract

Complex Enriques surfaces with a finite group of automorphisms are classified into seven types. In this paper, we determine which types of such Enriques surfaces exist in characteristic 2. In particular we give a one dimensional family of classical and supersingular Enriques surfaces with the automorphism group isomorphic to the symmetric group of degree five.