Vanesa Caruso, Licia Iacoviello, Augusto Di Castelnuovo, Sergio Storti, Guglielmo Mariani, Giovanni de Gaetano, Maria Benedetta Donati. Laboratory of Genetic and Environmental Epidemiology, Research Laboratories, and Hematology-Oncology Unit, Centre for High Technology Research and Education in Biomedical Sciences, Catholic University, Campobasso, Division of Hematology, L’Aquila University, L’...

Let G be a bipartite graph with edge ideal I(G) whose quotient ring R/I(G) is sequentially Cohen-Macaulay. We prove: (1) the independence complex of G must be vertex decomposable, and (2) the Castelnuovo-Mumford regularity of R/I(G) can be determined from the invariants of G.

The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connections between two recent definitions of multigraded regularity with a view towards a better understanding of the multigraded Hilbert function of fat point schemes in P1 × · · · × Pk . MSC 2000: 13D02, ...

We give a new short proof of the fact that the CastelnuovoMumford regularity of a strongly stable ideal is the highest degree of a minimal monomial generator. Our proof depends on results due to D. Maclagan and G. Smith on multigraded regularity. More precisely, we construct a Stanley filtration for strongly stable ideals which provides a bound for the Castelnuovo-Mumford regularity.

Let $$\mathcal {D}$$ be a weighted oriented graph and let $$I(\mathcal {D})$$ its edge ideal in polynomial ring R. We give the formula of Castelnuovo–Mumford regularity $$R/I(\mathcal when is path or cycle such that edges are one direction. Additionally, we compute projective dimension for this class graphs.