Reduction numbers, Rees algebras and Pfaffian ideals
type: Item
instance of: scholarly article
title: Reduction numbers, Rees algebras and Pfaffian ideals
zbMATH Open document ID: 0838.13003
DOI: 10.1016/0022-4049(94)00069-U
author: Ian M. Aberbach
author: Sam Huckaba
author: Craig Huneke
published in: Journal of Pure and Applied Algebra
publication date: 1996-06-03T00:00:00Z
review text: This paper is concerned with practical methods of testing the Cohen-Macaulay property of the Rees algebra or the form ring of an ideal \(I\) in a Cohen-Macaulay (or Gorenstein) local ring \(R\). In theorem 2.2 the authors establish bounds on the reduction numbers of certain ideals \(I \subset R\) (e.g. unmixed, generically a complete intersection of analytic deviation 1) with Cohen-Macaulay form ring -- via a presentation matrix of \(I\). The main application of theorem 2.2 and its corollaries is to a family of 5-generated height 3 Gorenstein ideals of a Gorenstein (in particular of a regular) local ring \(R\) in theorem 3.1. An analogue of this theorem is given in theorem 2.11 for 4-generated height 2 Cohen-Macaulay ideals \(I\) of a Cohen-Macaulay local ring \(R\).
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 810220
zbMATH Keywords: Cohen-Macaulay property of the Rees algebra
zbMATH Keywords: form ring
zbMATH Keywords: reduction numbers
zbMATH Keywords: 5-generated height 3 Gorenstein ideals
reviewed by: Manfred Herrmann
MaRDI profile type: Publication
cites work: An improved Briançon-Skoda theorem with applications to the Cohen- Macaulayness of Rees algebras
cites work: Graded algebras of powers of ideals generated by A-sequences
cites work: Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
cites work: Q5560333
cites work: Q3877802
cites work: On Graded Rings Associated to Analytic Deviation One Ideals
cites work: Q4295719
cites work: Approximation complexes of blowing-up rings
cites work: Approximation complexes of blowing-up rings. II
cites work: On complete d-sequences and the defining ideals of Rees algebras
cites work: Powers of Ideals Having Small Analytic Deviation
cites work: Rees Algebras of Ideals Having Small Analytic Deviation
cites work: On the associated graded ring of an ideal
cites work: Linkage and the Koszul Homology of Ideals
cites work: Q3356408
cites work: The \(S_ 2\)-closure of a Rees algebra
cites work: Q5829838
cites work: Liaison des variétés algébriques. I
cites work: On the associated graded ring of a local Cohen-Macaulay ring
cites work: The Syzygies of the Conormal Module
cites work: Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
cites work: The equations of Rees algebras of ideals with linear presentation
cites work: Certain graded algebras are always Cohen-Macaulay
cites work: On the equations of Rees algebras.
description: scientific article; zbMATH DE number 810220