Related papers: Reduced arithmetically Gorenstein schemes and simp…

We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which…

We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if $\mathcal H$ is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein $k$-algebras with the weak Lefschetz property…

For a standard Artinian $k$-algebra $A=R/I$, we give equivalent conditions for $A$ to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of the generic initial ideal…

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal…

We deal with the Weak Lefschetz property (WLP) for Artinian standard graded Gorenstein algebras of codimension $3.$ We prove that many Gorenstein sequences force the WLP for such algebras. Moreover for every Gorenstein sequence $H$ of…

We study the Artinian reduction $A$ of a configuration of points $X \subset {\mathbb P}^n $, and the relation of the geometry of $X$ to Lefschetz properties of $A$. Migliore initiated the study of this connection, with a particular focus on…

It has been conjectured that {\it all} graded Artinian Gorenstein algebras of codimension three have the weak Lefschetz property over a field of characteristic zero. In this paper, we study the weak Lefschetz property of associated graded…

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in $[Wi]$)…

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle…

A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated…

Codimension two Artinian algebras $A$ have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras -…

We study the free resolutions of some Artin Gorenstein algebras of Hilbert function $(1,4,k,k,4,1)$ and we prove that all such algebras have the Strong Lefschetz property if they have the Weak Lefschetz property. In the case $k=4$ we prove…

In this paper we study the Weak Lefschetz property of two classes of standard graded Artinian Gorenstein algebras associated in a natural way to the Ap\'ery set of numerical semigroups. To this aim we also prove a general result about the…

It is known that all complete intersection Artinian standard graded algebras of codimension 3 have the Weak Lefschetz Property. Unfortunately, this property does not continue to be true when you increase the number of minimal generators for…

In a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian…

We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level…

We study the weak Lefschetz property of a class of graded Artinian Gorenstein algebras of codimension three associated in a natural way to the Ap\'ery set of a numerical semigroup generated by four natural numbers. We show that these…

We introduce the $k$-strong Lefschetz property ($k$-SLP) and the $k$-weak Lefschetz property ($k$-WLP) for graded Artinian $K$-algebras, which are generalizations of the Lefschetz properties. The main results obtained in this paper are as…

The basic sequence of a homogeneous ideal $I\sset R=k[\seq{x}{1}{r}]$ defining an Artinian graded ring $A=R/I$ not having the weak Lefschetz property has the property that the first term of the last part is less than the last term of the…

We study the weak Lefschetz property of artinian Gorenstein algebras and in particular of artinian complete intersections. In codimension four and higher, it is an open problem whether all complete intersections have the weak Lefschetz…