The space of Cohen-Macaulay curves

Sequentially Cohen-Macaulay Graphs of Form θ_{n1, ...nk}

A characterization of shellable and sequentially Cohen-Macaulay

We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.

A Speciality Theorem for Cohen-macaulay Space Curves

We prove a version of the Halphen Speciality Theorem for locally Cohen-Macaulay curves in P3. To prove the theorem, we strengthen some results of Okonek and Spindler on the spectrum of the ideal sheaf of a curve. As an application, we classify curves C having index of speciality as large as possible once we fix the degree of C and the minimum degree of a surface

THE CONCEPT OF (I; J)-COHEN MACAULAY MODULES

‎We introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎We also introduce the concept of $(I,J)$-Cohen--Macaulay modules as a generalization of concept of Cohen--Macaulay modules‎. ‎These kind of modules are different from Cohen--Macaulay modules‎, as an example shows‎. ‎Also an art...

Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module

Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...