On the generic free resolutions
type: Item
instance of: scholarly article
title: On the generic free resolutions
zbMATH Open document ID: 0688.13003
DOI: 10.1016/0021-8693(90)90042-M
author: Piotr Pragacz
author: Jerzy Weyman
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: With the aid of structure theorems by Buchsbaum and Eisenbud for finite free resolutions, Hochster has given a universal pair for resolutions of \(length\quad 2.\) This means a ring R and a resolution \({\mathbb{F}}\) over R such that for each resolution \({\mathbb{G}}\) of the same size over a ring S there is a unique map \(R\to S\) so that \({\mathbb{G}}={\mathbb{F}}\otimes_ RS.\) Hochster proved that R is a noetherian normal CM-ring. - In this paper the authors consider the same problem for resolutions of \(length\quad 3.\) For resolutions of type (1,n,n,1) a generic ring is found, i.e. Hochster's result is generalized but for unicity. The authors conjecture that the ring is noetherian. The paper is highly technical by necessity. The methods used come from combinatorics and algebraic geometry.
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 4127354
zbMATH Keywords: generic free resolutions
MaRDI profile type: Publication
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full work available at URL: 0021-8693(90)90042-m
OpenAlex ID: W2054806382
description: scientific article; zbMATH DE number 4127354