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arXiv · 1210.6254

Singularities of varieties admitting an endomorphism

Amaël Broustet·Andreas Höring
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Abstract

Let X be a normal variety such that $K_X$ is Q-Cartier, and let $f: X \rightarrow X$ 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. As a consequence we prove that if X is projective and f polarised, then X has at most log-canonical singularities.

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Amaël Broustet, Andreas Höring. 2012-10-23. Singularities of varieties admitting an endomorphism. https://arxiv.org/abs/1210.6254

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