Nearly Gorenstein cyclic quotient singularities

Abstract

We investigate the nearly Gorenstein property among d-dimensional cyclic quotient singularities Bbbk llbracket x_1,dots ,x_drrbracket ^G, where Bbbk is an algebraically closed field and Gsubseteq {text {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.