Maximal Cohen-Macaulay modules over the cone of an elliptic curve
type: Item
instance of: scholarly article
title: Maximal Cohen-Macaulay modules over the cone of an elliptic curve
zbMATH Open document ID: 1056.14048
DOI: 10.1016/S0021-8693(02)00052-2
author: Radu Laza
author: Gerhard Pfister
author: Dorin Popescu
published in: Journal of Algebra
publication date: 2002-11-28T00:00:00Z
review text: Let \(k\) be an algebraically closed field with \(\text{char\,} k \neq 3\) and \(R = k[Y_1, Y_2, Y_3]/(Y_1^3 + Y_2^3 + Y_3^3)\). In the present article, the authors compute all the indecomposable Cohen-Macaulay \(R\)-modules of dimension~\(2\). Since~\(R\) is normal, it is equivalent to computing vector bundles over a curve \(\text{Proj} R\). The curve \(\text{Proj} R\) is an elliptic curve and \textit{M. F. Atiyah} [Proc. Lond. Math. Soc., III. Ser. 7, 414--452 (1957; Zbl 0084.17305)] classified vector bundles over such a curve. The novelty of this article is having computed free resolutions of such modules explicitly. The authors use the computer algebra system SINGULAR. This article contains some programmes.
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 1836726
zbMATH Keywords: vector bundle
zbMATH Keywords: matrix factorization
zbMATH Keywords: SINGULAR
describes a project that uses: SINGULAR
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00052-2
OpenAlex ID: W2124837846
description: scientific article; zbMATH DE number 1836726