Enriques surfaces with eight nodes

Abstract

A nodal Enriques surface can have at most 8 nodes. We give an explicit description of Enriques surfaces with 8 nodes, showing that they are quotients of products of elliptic curves by a group isomorphic to ${\mathbb{Z}}_2^2$ or to ${\mathbb{Z}}_2^3$ acting freely in codimension 1. We use this result to show that if $S$ is a minimal surface of general type with $p_g=0$ such that the image of the bicanonical map is birational to an Enriques surface then $K_S^2=3$ and the bicanonical map is a morphism of degree 2.

Latex 2e, 11 pages