On the structure of Gorenstein ideals of deviation two
type: Item
instance of: scholarly article
title: On the structure of Gorenstein ideals of deviation two
zbMATH Open document ID: 0854.13009
DOI: 10.1007/BF03322208
author: Craig Huneke
author: Bernd Ulrich
author: Wolmer V. Vasconcelos
published in: Results in Mathematics
publication date: 1996-05-01T00:00:00Z
review text: In this article, the authors prove: Theorem 3.1. Let \((R, {\mathfrak m})\) be a regular local ring with infinite residue field, let \(I\subset {\mathfrak m}^2\) be a reduced Gorenstein ideal of deviation two such that \(\dim R/I= 2\), \(I\) is a complete intersection locally on the punctured spectrum and \(T^2 (R/ I)= 0\). If \(I^k\) is integrally closed for some \(k\geq 3\), then \(g= \text{grade } I\) is odd, and \(I\) is a Huneke-Ulrich ideal, i.e., there exist a \(g+1\) by 1 matrix \(X\) and an alternating \(g+1\) by \(g+1\) matrix \(Y\) both of which have entries in \({\mathfrak m}\) such that \(I= I_1 (Y\cdot X)+ Pf (Y)\). Corollary 3.2. Let \((R, {\mathfrak m})\) be a regular local ring with infinite residue field, let \(I \subset {\mathfrak m}^2\) be a reduced Gorenstein ideal of deviation two such that \(\dim R/I= 2\), \(I\) is a complete intersection locally on the punctured spectrum and \(I\) is licci. If \(I^k\) is integrally closed for some \(k\geq 3\), then \(g= \text{grade } I\) is odd, and \(I\) is a Huneke-Ulrich ideal.
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13C14
zbMATH DE Number: 872702
zbMATH Keywords: syzygy
zbMATH Keywords: linkage
zbMATH Keywords: regular local ring
zbMATH Keywords: deviation
zbMATH Keywords: Huneke-Ulrich ideal
zbMATH Keywords: Gorenstein ideal
zbMATH Keywords: complete intersection
reviewed by: Jun Nishimura
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322208
OpenAlex ID: W2082788009
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description: scientific article; zbMATH DE number 872702