On the structure of normal projective surfaces admitting non-isomorphic surjective endomorphisms

Abstract

Normal projective surfaces admitting non-isomorphic surjective endomorphisms are classified up to isomorphism except singular rational surfaces with only quotient singularities and with big anti-canonical divisor. A surface in our list admits a finite Galois cover étale in codimension 1 from one of the following surfaces: a toric surface with Galois invariant open torus, an abelian surface, a P1-bundle over an elliptic curve, a projective cone over an elliptic curve, and the direct product of a non-singular projective curve of genus at least 2 and of a rational or elliptic curve.