École polytechnique – Centre de Physique Théorique, salle Jean Lascoux (aile 0)

10h30 – Shou Yoshikawa (Tokyo)

"Singularities of non-Q-Gorenstein varieties admitting a polarized endomorphism"

Résumé : Polarized endomorphisms are classical objects and studied a long time. Broustet and Höring proved that if X is Q-Gorenstein and has non-invertible polarized endomorphism, then X has at worst log canonical singularities. In this talk, I will prove a generalization of this result for non-Q-Gorenstein varieties. One of the key notions of the proof of this theorem is valuative log canonical singularieties. It is a kind of generalizations of log canonical singularietis for non-Q-Gorenstein varieties. I will introduce examples and properties of valuative log canonical singularities. I will also define other generalizatins of log canonical singularieties and discuss the difference between each other.