Structure of Fano fibrations of varieties admitting an int-amplified endomorphism

Abstract

In this paper, we study the structure of Fano fibrations of varieties admitting an int-amplified endomorphism. We prove that if a normal Q-factorial klt projective variety X has an int-amplified endomorphism, then there exists an étale in codimension one finite morphism X˜→X such that X˜ is of Fano type over its Albanese variety. As a corollary, if we further assume that X is smooth and rationally connected, then X is of Fano type.