# Singularities of varieties admitting an endomorphism

@article{Broustet2012SingularitiesOV,
title={Singularities of varieties admitting an endomorphism},
author={Ama{\"e}l Broustet and Andreas H{\"o}ring},
journal={Mathematische Annalen},
year={2012},
volume={360},
pages={439-456}
}
• Published 23 October 2012
• Mathematics
• Mathematische Annalen
Let $$X$$X be a normal variety such that $$K_X$$KX is $$\mathbb {Q}$$Q-Cartier, and let $$f:X \rightarrow X$$f:X→X be a finite surjective morphism of degree at least two. We establish a close relation between the irreducible components of the locus of singularities that are not log-canonical and the dynamics of the endomorphism $$f$$f. As a consequence we prove that if $$X$$X is projective and $$f$$f polarised, then $$X$$X has at most log-canonical singularities.
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