Related papers: A stable property of Borel type ideals

We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in Stahl-Totik sense.

Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I[x] for some ideals I of R.

Strongly stable ideals are a class of monomial ideals which correspond to generic initial ideals in characteristic zero and can be described completely by their Borel generators, a subset of the minimal monomial generators of the ideal.…

When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…

In the first chapter we present new results related on monomial ideals of Borel type. Also, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we extend several results…

We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…

We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main…

Let n,d be positive integers, with d even (say d=2e). Let X_(n,d) denote the locus of degree d hypersurfaces in P^n which consist of two e-fold hyperplanes. We bound the regularity of the ideal of this variety. Moreover, we show that this…

We study ideals of Borel type, including $k$-Borel ideals and $t$-spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated squarefree principal…

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S=k[x_1,x_2,...,x_n]; this includes the case of…

Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.

We prove existence results for nodal solutions of the Yamabe equation that are constant along the level sets of an isoparametric function.

The goal of this short note is to prove that when $A$ is a closed *-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an isomorphism from the…

We prove that there are energetically stable bimetric theories. These theories satisfies a positive energy theorem. We construct a model example.

In the framework of variable exponent Sobolev spaces, we prove that the variational eigenvalues defined by inf sup procedures of Rayleigh ratios for the Luxemburg norms are all stable under uniform convergence of the exponents.

We prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular and give a cellular structure for it. This shows that this resolution is a generalization of the well known Eliahou-Kervaire resolution for stable ideals in a…

A theorem of the Kolmogorov--Chentsov type is proved for random fields on a Riemannian manifold.

A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…

In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an…

In this paper it is shown that a sortable ideal $I$ is Freiman if and only if its sorted graph is chordal. This characterization is used to give a complete classification of Freiman principal Borel ideals and of Freiman Veronese type ideals…