Normal forms for quasi-elliptic Enriques surfaces and applications

Abstract

We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application is the completion of the classification of Enriques surfaces with finite automorphism groups started by Kondo, Nikulin, Martin and Katsura-Kondo-Martin.

On extra-special Enriques surfaces

“…For Claim (3), note that with the alternative description given in Claim (1), surfaces of type D6 ⊕ Ã1 have first been constructed in [8,Example 7.9] and the conjectural number of moduli for these surfaces given in [8,Corollary 7.8] has recently been confirmed to be 2 in [12,Proposition 14.1].…”