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 étale in codimension one finite morphism $\tilde{X}\to X$ such that $\tilde{X}$ 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.

中文翻译：

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承认内部放大内同态的品种的 Fano 纤维结构

在本文中，我们研究了允许内部放大自同态的品种的 Fano 纤维结构。我们证明如果一个正常的$\mathbb{问}$-阶乘 klt 射影簇X有一个整数放大的内同态，那么在余维一有限态射中存在一个 étale$\stackrel{～}{X}\to X$ 以至于 $\stackrel{～}{X}$在其 Albanese 品种上属于 Fano 类型。作为推论，如果我们进一步假设X是平滑且有理连接的，那么X是 Fano 类型的。