# Typical sheaves of generalized CM-modules

Brodmann, M (1992). Typical sheaves of generalized CM-modules. Manuscripta Mathematica, 76(1):181-192.

## Abstract

Let $M$ be a generalized Cohen-Macaulay module over a Noetherian local ring $(R,{\germ m})$. Fix a standard system of parameters $x_1,\cdots, x_d \in {\germ m}$ with respect to $M$ and let $I=\sum^d_{i=1} x_i R$. In this paper, we construct a coherent Cohen-Macaulay sheaf ${\scr K}$ over the projective space ${\bf P}^{d-1}_{R/I}$ whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules $H^i_{\germ m} (M)$ $(i=0,\cdots, d-1)$.

## Abstract

Let $M$ be a generalized Cohen-Macaulay module over a Noetherian local ring $(R,{\germ m})$. Fix a standard system of parameters $x_1,\cdots, x_d \in {\germ m}$ with respect to $M$ and let $I=\sum^d_{i=1} x_i R$. In this paper, we construct a coherent Cohen-Macaulay sheaf ${\scr K}$ over the projective space ${\bf P}^{d-1}_{R/I}$ whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules $H^i_{\germ m} (M)$ $(i=0,\cdots, d-1)$.