On Gorenstein surfaces dominated by {${\bf P}\sp 2$}

Abstract

In this paper we prove that a normal Gorenstein surface dominated by $\mathbf{P}2$ is isomorphic to a quotient $\mathbf{P}^2/G$, where $G$ is a finite group of automorphisms of $\mathbf{P}^2$ (except possibly for one surface $V_8'$). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.