Classification of Enriques surfaces covered by the supersingular $K3$ surface with Artin invariant 1 in characteristic 2

Coble surfaces with finite automorphism group

“…(12) : u 0 v 0 − u 1 v 1 = 0 (p 4 , p 8 , p 9 , p 10 ), (13) : (12,34,56) : u 0 v 1 + u 1 v 0 = 0 (p 1 , p 3 , p 5 , p 7 ), (12,35,46) : (12,36,45) : (13,24,56) : u 0 v 0 − ζ 2 u 1 v 1 = 0 (p 1 , p 5 , p 9 , p 10 ), (13,25,46) : (13,26,45) : (14,23,56) : (14,25,36) : (14,26,35) : (15,23,46) : (15,24,36) : (15,26,34) : (16,23,45) : (16,24,35) : (16,25,34) :…”

“…The Coble surfaces of type MI, MII are suggested by Mukai and Ohashi [19]. There are several Enriques surfaces with infinite group of automorphisms whose nef cones contain the same finite polytope defined by 40 roots as in the case of Coble surfaces of MI, MII (see Kondō [15], Mukai and Ohashi [18]). In these cases only a part of 40 roots are realized by (−2)curves.…”