SINGULARITY OF NORMAL COMPLEX ANALYTIC SURFACES ADMITTING NON-ISOMORPHIC FINITE SURJECTIVE ENDOMORPHISMS

For a non-isomorphic finite endomorphism of a germ of a complex analytic normal surface at a point, the pair of the surface and a completely invariant reduced divisor is shown to be log-canonical. It is also shown in many situations that the endomorphism or its square lifts to an endomorphism of another surface by an essential blowing up.