Nearly Gorenstein cyclic quotient singularities

Abstract

We investigate the nearly Gorenstein property among $d$-dimensional cyclic quotient singularities $\Bbbk[[x_1,\dots,x_d]]^G$, where $\Bbbk$ is an algebraically closed field and $G\subseteq{\rm GL}(d,\Bbbk)$ is a finite small cyclic group whose order is invertible in $\Bbbk$. We prove a necessary and sufficient condition to be nearly Gorenstein that also allows us to find several new classes of such rings.