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J. Lipman proved that the last Hilbert–Samuel coefficient of normal ideals of a 2-dimensional complete local ring R are bounded by the geometric genus of X=Spec(R). In this paper we extend this result to ideals I of a d-dimensional Cohen–Macaulay local ring R such that the associated graded ring of R with respect to In is Cohen–Macaulay for n≫0. We study the ideals such that their last Hilbert–Samuel...
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