On associated graded modules having a pure resolution

2014/09/05 by Puthenpurakal, Tony J.
#Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A30 #Secondary 13D02

paper · doi:10.48550/arxiv.1409.1762

Abstract

Let A = K[[X₁,⋯,X_n]] and let \mathfrakm = (X₁,⋯,X_n). Let M be a Cohen-Macaulay A-module of codimension p. In this paper we give a necessary and sufficient condition for the associated graded module G_\mathfrakm(M) to have a pure resolution over the polynomial ring G_\mathfrakm(A) ≅ K[X₁,⋯,X_n].

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