We give several characterizations for the linearity property for a maximal Cohen-Macaulay module over a local or graded ring, as well as proofs of existence in some new cases. In particular, we prove that the existence of such modules is preserved when taking Segre products, as well as when passing to Veronese subrings in low dimensions. The former result even yields new results on the existenc...

We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes X and Y : If they intersect properly in an arithmetically Cohen-Macaulay subsc...

A certain inequality is shown to hold for the values of the Möbius function of the poset obtained by attaching a maximum element to a lower Eulerian Cohen– Macaulay poset. In two important special cases, this inequality provides partial results supporting Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjec...

In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General biCohen-Macaulay graphs are classified up to separation. The inseparable bi-CohenMacaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.

We prove that for d ≥ 3, the 1-skeleton of any (d− 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette’s lower bound inequalities for boundary complexes of simplicial polytopes ([4],[3]) hold for every 2-CM complex of dimension ≥ 2 (see Kalai [8]). Moreover, the initial part (g0, g1, g2) of the g-vector of a 2-CM complex (of dimensio...

In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a new poset fiber theorem, for doubly homo...

For a finitely generated A-module M we define the dimension filtration M = {Mi}0≤i≤d, d = dimA M, where Mi denotes the largest submodule of M of dimension ≤ i. Several properties of this filtration are investigated. In particular, in case the local ring (A,m) possesses a dualizing complex, then this filtration occurs as the filtration of a spectral sequence related to duality. Furthermore, we c...

Abstract. Criteria are given in terms of certain Hilbert coefficients for the fiber cone F (I) of an m-primary ideal I in a Cohen-Macaulay local ring (R,m) so that it is Cohen-Macaulay or has depth at least dim(R) − 1. A version of Huneke’s fundamental lemma is proved for fiber cones. Goto’s results concerning Cohen-Macaulay fiber cones of ideals with minimal multiplicity are obtained as conseq...

It is a well known fact that a supersolvable lattice is ELoshellable. Hence a supersolvable lattice (resp., its Stanley-Reisner ring) is Cohen-Macaulay. We prove that if L is a supersolvable lattice such that all intervals have non-vanishing Mt~bius number, then for an arbitrary element x e L the poser L {x} is also Cohen-Macaulay. Posets with this property are called 2-Cohen-Macaulay posets. I...

For a skew version of graded (A ∞ ) hypersurface singularity A, we study the stable category maximal Cohen-Macaulay modules over A. As consequence, see that A has countably infinite Cohen–Macaulay representation type and is not noncommutative isolated singularity.