On normal Moishezon surfaces admitting non-isomorphic surjective endomorphisms

Abstract

Normal Moishezon surfaces admitting non-isomorphic surjective endomorphisms are classified in some cases by using the original notion: "characteristic completely invariant divisor." A surface in our list has a finite Galois cover étale in codimension 1 from one of the following surfaces: a toric surface, 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 ≥ 2 with a rational or elliptic curve. As a corollary of our classification, any normal Moishezon surface admitting non-isomorphic surjective endomorphisms is shown to be projective.