Free resolutions of certain codimension three perfect radical ideals
type: Item
instance of: scholarly article
title: Free resolutions of certain codimension three perfect radical ideals
zbMATH Open document ID: 0658.13013
DOI: 10.1007/BF01324720
author: J. F. Andrade
author: Aron Simis
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: The main purpose of this work is to enrich the knowledge of codimension three radical ideal by means of understanding their syzygy-theoretic and analytic properties. The class of ideals envisaged here comprise ideals of maximal (generic) minors fixing a submatrix and presentation ideals of some of the derived blowing-up algebras. The main results obtained concern the free resolutions and the complete intersection locus of such ideals. A central technique, used but not fully developed here, is that of cutting sizes of tensor product of maps by means of appropriate trace maps. Some of the instances considered may serve as testing ground for Vasconcelos' conjectures, beyond the realm of pure resolutions.
Mathematics Subject Classification ID: 13D99
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13A10
zbMATH DE Number: 4075245
zbMATH Keywords: codimension three radical ideals
zbMATH Keywords: blowing-up algebras
zbMATH Keywords: free resolutions
zbMATH Keywords: complete intersection locus
zbMATH Keywords: Vasconcelos' conjectures
zbMATH Keywords: Rees algebras
MaRDI profile type: Publication
cites work: A Complex That Resolves the Ideal of Minors Having n - 1 Columns in Common
cites work: On ideals of minors fixing a submatrix
cites work: Some structure theorems for finite free resolutions
cites work: Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
cites work: A Generalized Koszul Complex. II. Depth and Multiplicity
cites work: Symmetric algebras of modules arising from a fixed submatrix of a generic matrix
cites work: Blow-up of Straightening-Closed Ideals in Ordinal Hodge Algebras
cites work: Ein Kriterium für vollständige Durchschnitte
cites work: Q5648459
cites work: On the associated graded ring of an ideal
cites work: Criteria for Complete Intersections
cites work: Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci
cites work: The dimension and components of symmetric algebras
cites work: Q3831115
cites work: On the divisor class group of Rees-algebras
cites work: Linkage theory for algebras with pure resolutions
cites work: Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
cites work: Complexes associated with trace and evaluation. Another approach to Lascoux's resolution
cites work: Q3765888
cites work: The divisor class group of ordinary and symbolic blow-ups
cites work: Koszul Homology and the Structure of Low Codimension Cohen-Macaulay Ideals
cites work: The complete intersection locus of certain ideals
description: scientific article; zbMATH DE number 4075245