Linkage theory for algebras with pure resolutions
type: Item
instance of: scholarly article
title: Linkage theory for algebras with pure resolutions
zbMATH Open document ID: 0602.13009
DOI: 10.1016/0021-8693(86)90137-7
author: Andrew Kustin
author: Bernd Ulrich
author: M. P. Miller
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let \(S=[k[X_ 1,...,X_ n]/I\) be a graded Cohen-Macaulay ring with k an infinite field. This pleasantly written paper proves that if S is generically a complete intersection and the minimal free resolution of S is pure and almost linear, then S is not in the linkage class of a complete intersection (apart from the known exceptions when S has codimension two, or S is Gorenstein of codimension three). When S has small codimension, more is said. For example, if S has codimension three and has a pure resolution, then S is the linkage class of a complete intersection if and only if S is Gorenstein. Results concerning what sequences of twists and Betti numbers can occur in minimal homogeneous resolutions of graded Cohen-Macaulay algebras are also given.
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 3970881
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: linkage class of a complete intersection
zbMATH Keywords: small codimension
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90137-7
OpenAlex ID: W2087775573
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description: scientific article; zbMATH DE number 3970881