In an earlier work, we gave (additive) categorification of Grassmannian cluster algebras using the category CM(A) Cohen-Macaulay modules for a certain Gorenstein order A. this paper, each tilting object in CM(A), construct compatible pair (B,L) way that is consistent with mutation. This then determines quantum algebra and show that, when comes from rank one summands, (generically) isomorphic to...

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 ........

We provide a criterion that for an equivalence group G on holomorphic germs, the discriminant of a G-versal unfolding is a free divisor. The criterion is in terms of the discriminant being Cohen– Macaulay and generically having Morse-type singularities. When either of these conditions fails, we provide a criterion that the discriminant have a weaker free* divisor structure. For nonlinear sectio...

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...