Enriques surfaces in characteristic 2 with a finite group of automorphisms

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 1-dimensional family of classical and supersingular Enriques surfaces with the automorphism group A u t ( X ) \mathrm {Aut}(X) isomorphic to the symmetric group S 5 \mathfrak {S}_5 of degree 5.