Singularities of non-$\mathbb{Q}$-Gorenstein varieties admitting a polarized endomorphism

Abstract

In this paper, we discuss a generalization of log canonical singularities in the non-$\mathbb{Q}$-Gorenstein setting. We prove that if a normal complex projective variety has a non-invertible polarized endomorphism, then it has log canonical singularities in our sense. As a corollary, we give an affirmative answer to a conjecture of Broustet and Höring.

21 pages. To appear in IMRN. This paper is revised about the following points that the assumption in Theorem 1.6 is removed, and Theorem 6.7, Definition 6.8 and Theorem 6.9 are added. Furthermore Section 7 is also added in version 4