Related papers: Artinian level algebras of low socle degree

The classification of local Artinian Gorenstein algebras is equivalent to the study of orbits of a certain non-reductive group action on a polynomial ring. We give an explicit formula for the orbits and their tangent spaces. We apply our…

In this paper we consider Artin local K-algebras with maximal length in the class of Artin algebras with given embedding dimension and socle type. They have been widely studied by several authors, among others by Iarrobino, Fr\"oberg and…

In this paper we study standard graded artinian level algebras, in particular those whose socle-vector has type 2. Our main results are: the characterization of the level $h$-vectors of the form $(1,r,...,r,2)$ for $r\leq 4$; the…

Let $\Delta$ be a simplicial complex on $V = \{x_1,...,x_n\}$, with Stanley-Reisner ideal $I_{\Delta}\subseteq R = k[x_1,...,x_n]$. The goal of this paper is to investigate the class of artinian algebras $A=A(\Delta,a_1,...,a_n)=…

Let R be a polynomial ring in r variables and D a dual ring upon which R acts as partial differential operators (classical apolarity). For a type two graded level Artinian algebras A=R/I, of socle degree j we consider the family of Artinian…

In this paper, we continue the study of which $h$-vectors $\H=(1,3,..., h_{d-1}, h_d, h_{d+1})$ can be the Hilbert function of a level algebra by investigating Artinian level algebras of codimension 3 with the condition…

In this paper we give an effective characterization of Hilbert functions and polynomials of standard algebras over an Artinian equicharacteristic local ring; the cohomological properties of such algebras are also studied. We describe…

We generalize Iarrobino's symmetric decomposition for the associated graded algebra of an Artinian Gorenstein algebra to a symmetric decomposition of finite-length self-dual modules over a local algebra, and we deduce consequences for the…

A relatively compressed algebra with given socle degrees is an Artinian quotient $A$ of a given graded algebra $R/\fc$, whose Hilbert function is maximal among such quotients with the given socle degrees. For us $\fc$ is usually a…

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for cactus varieties of the third Veronese embedding.…

Macaulay's inverse system is an effective method to construct Artinian K-algebras with additional properties like, Gorenstein, level, more generally with any socle type. Recently, Elias and Rossi gave the structure of the inverse system of…

The Hilbert functions and the regularity of the graded components of local cohomology of a bigraded algebra are considered. Explicit bounds for these invariants are obtained for bigraded hypersurface rings.

Let $A$ be an Artinian Gorenstein algebra over an infinite field $k$ with either $\hbox{char}(k)=0$ or $\hbox{char}(k)>\nu$, where $\nu$ is the socle degree of $A$. To every such algebra and a linear projection $\pi$ on its maximal ideal…

Let $R=k[x_1,..., x_r]$ be the polynomial ring in $r$ variables over an infinite field $k$, and let $M$ be the maximal ideal of $R$. Here a \emph{level algebra} will be a graded Artinian quotient $A$ of $R$ having socle $Soc(A)=0:M$ in a…

In this paper we study the O-sequences of the local (or graded) $K$-algebras of socle degree $4.$ More precisely, we prove that an O-sequence $h=(1, 3, h_2, h_3, h_4)$, where $h_4 \geq 2,$ is the $h$-vector of a local level $K$-algebra if…

The Hilbert function of standard graded algebras are well understood by Macaulay's theorem and very little is known in the local case, even if we assume that the local ring is a complete intersection. An extension to the power series ring…

It is unknown if an Artinian level O-sequence of codimension 3 and type $r (\ge 2)$ is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of…

We find a sufficient condition that $\H$ is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function $\H=(h_0,h_1,..., h_{d-1}>h_d=h_{d+1})$ cannot be level if…

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 -…

In singularity theory or algebraic geometry, it is natural to investigate possible Hilbert functions for special algebras $A$ such as local complete intersections or more generally Gorenstein algebras. The sequences that occur as {the}…