Symbolic powers, Serre conditions and Cohen-Macaulay Rees algebras
type: Item
instance of: scholarly article
title: Symbolic powers, Serre conditions and Cohen-Macaulay Rees algebras
zbMATH Open document ID: 0829.13003
DOI: 10.1007/BF02567981
author: Susan Morey
author: Sunsook Noh
author: Wolmer V. Vasconcelos
published in: Manuscripta Mathematica
publication date: 1996-01-17T00:00:00Z
full work available at URL: https://eudml.org/doc/156041
review text: Let \(R\) be a local Cohen-Macaulay ring and \(I\) an unmixed ideal of \(R\) which is generically a complete intersection and satisfies \(I^{(n)} = I^n\) for all \(n \geq 1\). This paper investigates when the Rees algebras \({\mathfrak R} = R[It]\) and the associated graded ring \(G = \text{gr}_I (R)\) are also Cohen-Macaulay. Several partial answers to these two questions are given in terms of when \(G\) satisfies the Serre condition \((S_r)\).
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13C40
zbMATH DE Number: 724679
zbMATH Keywords: Cohen-Macaulay property of associated graded ring
zbMATH Keywords: local Cohen-Macaulay ring
zbMATH Keywords: complete intersection
zbMATH Keywords: Rees algebras
zbMATH Keywords: Serre condition
reviewed by: David F. Anderson
MaRDI profile type: Publication
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OpenAlex ID: W1966371258
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description: scientific article; zbMATH DE number 724679