Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the h-triangle, a doubly-indexed generalization of the h-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generaliz...

et  be a commutative Noetherian ring,  and  two ideals of  and  a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal  (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to  with ........

In this paper, we discuss some necessary and sufficient conditions for a curve to be arithmetically Cohen-Macaulay, in terms of its general hyperplane section. We obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically Cohen-Macaulay curve of P. We prove that almost all the degree matrices with positive s...

This paper addresses problems related to the existence of arithmetic Macaulayfications of projective schemes. Let Y be the blow-up of a projective scheme X = Proj R along the ideal sheaf of I ⊂ R. It is known that there are embeddings Y ∼ = Proj k[(I e) c ] for c ≥ d(I)e + 1, where d(I) denotes the maximal generating degree of I, and that there exists a Cohen-Macaulay ring of the form k[(I e) c...

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...