Monomial ideals whose depth function has any given number of strict local maxima

Monomial ideals of minimal depth

Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley’s conjecture holds for these ideals. Also we show that if I is a monomial ideal with Ass(S/I) = {P1, P2, . . . , Ps} and Pi 6⊂ ∑s 1=j 6=i Pj for all i ∈ [s], then Stanley’s conjecture holds for S/

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.

Monomial Ideals with Linear Quotients Whose Taylor Resolutions Are Minimal

We study when Taylor resolutions of monomial ideals are minimal, particularly for ideals with linear quotients.

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...