Smooth points of \(\text{Gor}(T)\)
type: Item
instance of: scholarly article
title: Smooth points of \(\text{Gor}(T)\)
zbMATH Open document ID: 0905.13004
DOI: 10.1016/S0022-4049(97)00052-2
published in: Journal of Pure and Applied Algebra
publication date: 1998-07-09T00:00:00Z
review text: Let \(R\) be an artinian Gorenstein algebra that is a graded quotient of \(k[x_0, x_1, \dots, x_n]\) (where \(k\) is an algebraically closed field of characteristic 0). \textit{Iarrobino} and \textit{Kanev} [``The length of a homogeneous form, determinantal loci of catalecticants and Gorenstein algebras'' (preprint)] have introduced the classifying spaces \(\text{Gor} (T)\) and \({\mathcal G}\)\textit{or}\((T)\) for \(R\) where \(T\) is a symmetric sequence. This paper deals with some of the problems concerning the dimension and smoothness of these spaces for the case \(n=3\), i.e., for artinian Gorenstein algebras of embedding dimension \(\leq 3\). A number of examples and results are given and some conjectures are made which are verified in several cases.
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 13E10
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1097605
zbMATH Keywords: artinian Gorenstein algebra
author: Anthony V. Geramita
author: Mario Pucci
author: Yong Su Shin
reviewed by: D. D. Anderson
MaRDI profile type: Publication
cites work: Q4838935
cites work: Nonunimodality of Graded Gorenstein Artin Algebras
cites work: A nonunimodal graded gorenstein artin algebra in codimension five
cites work: Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
cites work: Standard bases of perfect homogeneous polynomial ideals of height 2
cites work: Q3832689
cites work: Q3348001
cites work: Irreducibility and dimension theorems for families of height 3 Gorenstein algebras
cites work: Q4882175
cites work: The Hilbert Function of a Reduced K -Algebra
cites work: Hyperplane sections of a smooth curve in P3
cites work: Reduced Gorenstein codimension three subschemes of projective space
cites work: Some examples of unimodal Gorenstein sequences
cites work: Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
cites work: A family of complexes associated to an almost alternating map, with applications to residual intersections
cites work: Q4764201
cites work: Liaison des variétés algébriques. I
cites work: Q4322963
cites work: On Hilbert functions of reduced and of integral algebras
cites work: Q5185003
cites work: Hilbert functions of graded algebras
description: scientific article; zbMATH DE number 1097605