Abstract
Abstract In this paper, we introduce a new generalization of log canonical singularities for non-$\mathbb{Q}$-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 Höring [ 6].
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