On associated graded modules having a pure resolution

Abstract:

Let $A = K[[X_1,\cdots ,X_n]]$ and let $\mathfrak {m}= (X_1,\cdots ,X_n)$. 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 $G_{\mathfrak {m}}(M)$ to have a pure resolution over the polynomial ring $G_{\mathfrak {m}}(A) \cong K[X_1,\cdots ,X_n]$.