Local Cohomology of Stanley–Reisner Rings with Supports in General Monomial Ideals

Local Cohomology of Stanley-reisner Rings with Supports in General Monomial Ideals

Local Cohomology at Monomial Ideals

Cohomology on Toric Varieties and Local Cohomology with Monomial Supports

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The ith local cohom...

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...

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...