Normal Quintic Surfaces which are Birationally Enriques Surfaces

Abstract

Let S be an Enriques surface over an algebraically closed field k of characteristic ^2. Then, equivalently, S is a non-singular projective surface with q(S)=pg(S) = Q and 2KS^Q. It is known (cf. Cossec [Co]) that every Enriques surface admits a morphism of degree one onto a surface of degree 10 in P with isolated rational double points, and also that every Enriques surface is birationally equivalent to a (non-normal) sextic surface in P. Then there arises the following problem: