Residual intersections and modules with Cohen-Macaulay Rees algebra
type: Item
instance of: scholarly article
title: Residual intersections and modules with Cohen-Macaulay Rees algebra
zbMATH Open document ID: 1482.13010
author: Alessandra Costantini
published in: Journal of Algebra
publication date: 2021-09-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1811.08402
review text: Let \(R\) be a Gorenstein local ring and \(E\) a finite, torsion-free \(R\)-module with a rank. In the paper under review the author provides sufficient conditions for the Rees algebra \(\mathcal{R}(E)\) of \(E\) to be Cohen-Macaulay. As a consequence she obtains sufficient conditions for the Rees algebra of an ideal to be Cohen-Macaulay, and hence recovers a result proved independently by textit{M. Johnson} and \textit{B. Ulrich} [Compos. Math. 103, No. 1, 7--29 (1996; Zbl 0866.13001)], and by \textit{S. Goto} et al. [Am. J. Math. 118, No. 6, 1197--1213 (1996; Zbl 0878.13002)]. In order to prove this result the author first obtains sufficient conditions for \(E\) to be of linear type. This is done by constructing a generic Bourbaki ideal \(I\) of \(E\) and exploiting properties of the residual intersections of \(I\). The author also recovers main results proved by \textit{K.-N. Lin} [Commun. Algebra 44, No. 9, 3673--3682 (2016; Zbl 1360.13014)].
reviewed by: Shreedevi K. Masuti
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 7396010
zbMATH Keywords: Rees algebra of module
zbMATH Keywords: Cohen-Macaulay property
zbMATH Keywords: generic Bourbaki ideals
zbMATH Keywords: residual intersections
MaRDI profile type: Publication
OpenAlex ID: W3189812264
arXiv ID: 1811.08402
cites work: Complete intersections and symmetric algebras
cites work: Residual intersections in Cohen-Macaulay rings
cites work: Q4274969
cites work: Hilbert functions, residual intersections, and residually \(S_2\) ideals
cites work: Cohen-Macaulayness of Special Fiber Rings
cites work: Core of projective dimension one modules
cites work: Ideals defined by matrices and a certain complex associated with them
cites work: What is the Rees algebra of a module?
cites work: Cohen-Macaulay graded rings associated to ideals
cites work: Approximation complexes of blowing-up rings
cites work: Approximation complexes of blowing-up rings. II
cites work: On the Arithmetic and Homology of Algebras of Linear Type
cites work: Ideals with sliding depth
cites work: Rees Algebras of Ideals Having Small Analytic Deviation
cites work: On the symmetric and Rees algebra of an ideal generated by a d-sequence
cites work: On the symmetric algebra of a module
cites work: On the associated graded ring of an ideal
cites work: Strongly Cohen-Macaulay Schemes and Residual Intersections
cites work: When is the rees algebra cohen—macaulay?
cites work: Q4893918
cites work: Castelnuovo Regularity and Graded Rings Associated to an Ideal
cites work: Cohen–Macaulayness of Rees Algebras of Modules
cites work: Artin-Nagata properties, minimal multiplicities, and depth of fiber cones
cites work: Q3739243
cites work: Liaison des variétés algébriques. I
cites work: Q4718901
cites work: \(j\)-multiplicity and depth of associated graded modules
cites work: Primary ideals with good associated graded ring
cites work: A conjecture of j. sally
cites work: On the associated graded ring of a local Cohen-Macaulay ring
cites work: Jacobian Dual Fibrations
cites work: Cohen-Macaulay Rees algebras and degrees of polynomial relations
cites work: Rees Algebras of Modules
cites work: Tangent algebras
cites work: On the dimension and integrality of symmetric algebras
cites work: Q4295734
cites work: Ideals Having the Expected Reduction Number
cites work: The equations of Rees algebras of ideals with linear presentation
cites work: Form rings and regular sequences
DOI: 10.1016/J.JALGEBRA.2021.07.022
description: scientific article