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 $\mathbb{Q}$-factorial klt projective variety $X$ has an int-amplified endomorphism, then there exists an \'etale in codimension one finite morphism $\widetilde{X} \to X$ such that $\widetilde{X}$ 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.