Characteristic cycles of local cohomology modules of monomial ideals

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...

Local Cohomology at Monomial 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...

0 Local cohomology , arrangements of subspaces and monomial ideals

If k is the field of complex numbers (or, more generally, a field of characteristic zero), the module H i I(R) is known to have a module structure over the Weyl algebra An(k), and one can therefore consider its characteristic cycle, denoted CC(H i I(R)) in this paper (see e.g. [2, I.1.8.5]). On the other hand, the arrangement X defines a partially ordered set P (X) whose elements correspond to ...

Ideals with Maximal Local Cohomology Modules

This paper finds its motivation in the pursuit of ideals whose local cohomology modules have maximal Hilbert functions. In [8], [9] we proved that the lexicographic (resp. squarefree lexicographic) ideal of a family of graded (resp. squarefree) ideals with assigned Hilbert function provides sharp upper bounds for the local cohomology modules of any of the ideals of the family. Moreover these bo...