The class group of a minimal model of a quotient singularity

Abstract

Let $V$ be a finite-dimensional vector space over the complex numbers and let $G\leq \operatorname{SL}(V)$ be a finite group. We describe the class group of a minimal model (that is, $\mathbb Q$-factorial terminalization) of the linear quotient $V/G$. We prove that such a class group is completely controlled by the junior elements contained in $G$.