Typical sheaves of generalized CM-modules

Abstract

Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x₁, …, x_d∈m with respect to M and let$I = \sum\limits_{i = 1}^d { \times _i R}$. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ ^d-1_R/I whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H ⁱ_m (M), (i=0, …, d−1).