We deal with a generalization of a Theorem of P. Gordan and M. Noether on hypersurfaces
with vanishing (first) Hessian. We prove that for any given N≥ 3, d≥ 3 and 2≤ k< d 2 there …

A polynomial is a direct sum if it can be written as a sum of two nonzero polynomials in some
distinct sets of variables, up to a linear change of variables. We analyze criteria for a …

Abstract Macaulay's Inverse System gives an effective method to construct Artinian
Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any …

Let k be an algebraically closed field and let HilbdG (PkN) be the open locus of the Hilbert
scheme Hilbd (PkN) corresponding to Gorenstein subschemes. We prove that HilbdG (PkN) …

We classify all possible $ h $-vectors of graded artinian Gorenstein algebras in socle degree
4 and codimension $\leq 17$, and in socle degree 5 and codimension $\leq 25$. We obtain …

Let, the polynomial ring over a field k. Several of the authors previously classified nets of
ternary conics and their specializations over an algebraically closed field, Abdallah et al.(Eur …

ON THE DEGREE TWO ENTRY OF A GORENSTEIN h-VECTOR AND A CONJECTURE OF
STANLEY 1. Introduction Gorenstein rings arise in many area Page 1 PROCEEDINGS OF THE …

The main goal of this paper is to characterize the Hilbert functions of all (artinian)
codimension 4 Gorenstein algebras that have at least two independent relations of degree …

STANLEY’S THEOREM ON CODIMENSION 3 GORENSTEIN h-VECTORS We consider
standard graded artinian algebras A = R/I, where R = k[x1, Page 1 PROCEEDINGS OF THE …

We determine new bounds on the entries of Gorenstein Hilbert functions, both in any fixed
codimension and asymptotically. Our first main theorem is a lower bound for the degree i+ 1 …