Graded isolated singularities appeal very naturally in algebraic projective
geometry (cf. [18]) or in variant theory of the binary polyhedral groups (
cf. [15], [17]). We define mock finitely generated modules ill the category
of graded modules and we use such graded modules which are also Gorenstein
injective (cf. [1], [2]) in this category to characterize graded isolated
Gorenstein singularities.