Nearly Gorenstein cyclic quotient singularities

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