Let be a set of ideals of a commutative Noetherian ring . We use the notion of -closure operation which is a semiprime closure operation on submodules of modules to introduce the class of -Laskerian modules. This enables us to investigate the set of associated prime ideals of certain -closed submodules of local cohomology modules.
Let be the greatest odd integer less than or equal to . In this paper we provide explicit formulae to compute -graded Betti numbers of the circulant graphs . We do this by showing that this graph is the product (or join) of the cycle by itself, and computing Betti numbers of . We also discuss whether such a graph (more generally, ) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or .
Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.
The Castelnuovo-Mumford regularity is one of the most important invariants in studying the minimal free resolution of the defining ideals of the projective varieties. There are some bounds on the Castelnuovo-Mumford regularity of the projective variety in terms of the other basic invariants such as dimension, codimension and degree. This paper studies a bound on the regularity conjectured by Hoa, and shows this bound and extremal examples in the case of divisors on rational normal scrolls.
The purpose of this paper is twofold. First, we give an upper bound on the order of a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we give an explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine a standard linking theorem. These results are tied together by the construction of sharp examples for the bound,...
By analogy with the projective, injective and flat modules, in this paper we study some properties of -Gorenstein projective, injective and flat modules and discuss some connections between -Gorenstein injective and -Gorenstein flat modules. We also investigate some connections between -Gorenstein projective, injective and flat modules of change of rings.