Singularities of Non-Q-Gorenstein Varieties Admitting a Polarized Endomorphism

In this paper, we introduce a new generalization of log canonical singularities for non-Q-Gorenstein varieties. 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 Horing [6].