Irreducibility and dimension theorems for families of height 3 Gorenstein algebras
type: Item
instance of: scholarly article
title: Irreducibility and dimension theorems for families of height 3 Gorenstein algebras
zbMATH Open document ID: 0882.13021
author: Susan J. Diesel
published in: Pacific Journal of Mathematics
publication date: 1996-08-28T00:00:00Z
review text: \(R\) is the ring \(k[x,y,z]\) where \(k\) is an algebraically closed field. The author shows that when a set \(D=(Q,P)\) of generator and relation degrees is given, the family \(\text{Gor}_D\) of Gorenstein algebras \(A=R/J\) with \(J\) having this set of generator and relation degrees is irreducible. By using deformation theory, one proves that when \(T\) is fixed the family \(\text{Gor}_T\) of Gorenstein algebras with Hilbert function \(T\) is irreducible. Then, one determines the maximum number of generators possible for an ideal determining a given Hilbert function. Finally, one investigates various methods for determining the dimension of \(\text{Gor}_T\), one makes a conjecture for this dimension and one proves this conjecture in many cases.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 910264
zbMATH Keywords: relation degrees
zbMATH Keywords: Gorenstein algebras
zbMATH Keywords: number of generators
zbMATH Keywords: Hilbert function
reviewed by: Vasile Brînzănescu
MaRDI profile type: Publication
full work available at URL: pjm.1996.172.365
OpenAlex ID: W1512093745
DOI: 10.2140/PJM.1996.172.365
description: scientific article; zbMATH DE number 910264