Abstract:We investigate the nearly Gorenstein property among d-dimensional cyclic quotient singularities $$\Bbbk \llbracket x_1,\dots ,x_d\rrbracket ^G$$
k
〚
x
1
,
⋯
,
x
d
〛
G
, where $$\Bbbk $$
k
is an algebraically closed field and $$G\subseteq {\text {GL}}(d,\Bbbk )$$
G
⊆
GL
(
d
,
k
)
is a finite small cyclic group whose order is invertible in $$\Bbbk $$
k
. We prove a necessary and sufficient condition to be nearly Gorenstein that also allows us to find several new classes of such rings.
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