Equations of blowups of ideals of codimension two and three
type: Item
instance of: scholarly article
title: Equations of blowups of ideals of codimension two and three
zbMATH Open document ID: 0864.14001
DOI: 10.1016/0022-4049(95)00087-9
author: Susan Morey
published in: Journal of Pure and Applied Algebra
publication date: 1997-06-30T00:00:00Z
review text: This paper is devoted to the study of the defining equations of blow-up algebras in some particular cases. Blow-up algebras often appear in algebraic geometry and represent fibrations of a variety. More precisely, the author provides a generating set for the equations of Rees algebras of a Cohen-Macaulay domain associated to an ideal \(I\) of codimension two. \(I\) is required to satisfy some additional conditions and the result depends on the parity of the dimension of the base ring. The main aim of section 3 of the paper is to prove this central result. The generating set is given in terms of the jacobian dual of a presentation matrix of \(I\). The jacobian dual of a matrix is introduced and studied in section 2. Finally in section 4, some remarks are given concerning the degrees of the generators of the defining ideal whenever \(I\) is a codimension three Gorenstein ideal.
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 14M07
zbMATH DE Number: 896555
zbMATH Keywords: defining equations of blow-up algebras
zbMATH Keywords: Rees algebras
zbMATH Keywords: Cohen-Macaulay domain
zbMATH Keywords: jacobian dual of a matrix
zbMATH Keywords: generators of the defining ideal
reviewed by: Carlos Galindo
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00087-9
OpenAlex ID: W2048922093
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description: scientific article; zbMATH DE number 896555