Small Quotient Minimal Log Discrepancies

Abstract

We prove that for each positive integer n, there exists a positive number ${\mathit{ϵ}}_{\mathit{n}}$ such that n-dimensional toric quotient singularities satisfy the ACC for MLDs on the interval $(0,{\mathit{ϵ}}_{\mathit{n}})$. In the course of the proof, we show a geometric Jordan property for finite automorphism groups of affine toric varieties.