Singularities of varieties admitting an endomorphism

Amaël Broustet (1) , Andreas Hoering (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LJAD - Laboratoire Jean Alexandre Dieudonné

Let be a normal variety such that is -Cartier, and let 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 . As a consequence we prove that if is projective and polarised, then has at most log-canonical singularities.

Domaines: Géométrie algébrique [math.AG]

Amaël Broustet, Andreas Hoering. Singularities of varieties admitting an endomorphism. Mathematische Annalen, 2014, 360 (1-2), pp.439-456. ⟨10.1007/s00208-014-1015-9⟩. ⟨hal-01294810⟩