Abelian coverings of the projective plane by Enriques surfaces

Abstract

We study abelian coverings of the projective plane by Enriques surfaces. We show that if the quotient space of an Enriques surface by a finite abelian group G is isomorphic to the projective plane, then the action of G on an Enriques surface is semi-symplectic, and G is isomorphic to $${\mathbb {Z}}/2{\mathbb {Z}}^{\oplus l}$$ where $$l=2,3$$ , or 4. Further, we give examples to $$l=2,3,4$$ .