Tameness of local cohomology of monomial ideals with respect to monomial prime ideals

Tameness of Local Cohomology of Monomial Ideals with Respect to Monomial Prime Ideals

In this paper we consider the local cohomology of monomial ideals with respect to monomial prime ideals and show that all these local cohomology modules are tame. Introduction Let R be a graded ring. Recall that a graded R-module N is tame, if there exists an integer j0 such that Nj = 0 for all j ≤ j0, or else Nj 6= 0 for all j ≤ j0. Brodmann and Hellus [4] raised the question whether for a fin...

Local Cohomology at Monomial Ideals

Monomial Ideals with Primary Components given by Powers of Monomial Prime Ideals

We characterize monomial ideals which are intersections of powers of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.

Prime Filtrations of Monomial Ideals and Polarizations

We show that all monomial ideals in the polynomial ring in at most 3 variables are pretty clean and that an arbitrary monomial ideal I is pretty clean if and only if its polarization I p is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex correspond...

Characteristic Cycles of Local Cohomology Modules of Monomial Ideals

In his paper Lyu G Lyubeznik uses the theory of algebraic D modules to study local cohomology modules He proves in particular that if R is any regular ring containing a eld of characteristic zero and I R is an ideal the local cohomology modules H i I R have the following properties i H m H i I R is injective where m is any maximal ideal of R ii inj dimR H i I R dimRH i I R iii The set of the as...