On the relation type of fiber cone
type: Item
instance of: scholarly article
title: On the relation type of fiber cone
zbMATH Open document ID: 1351.13004
author: A. V. Jayanthan
author: Ramakrishna Nanduri
published in: Acta Mathematica Vietnamica
publication date: 2015-10-20T00:00:00Z
review text: Let \(I\) be an ideal in a Noetherian ring. The authors consider the Fiber Cone \(F(I)\) and the Rees algebra \({\mathcal R}(I)\) associated to \(I\), and study the relation type of these two algebras. First they prove that if \(I\) is a lexsegment ideal in a ring in two variables, then \(\operatorname{reltype}(F(I)) = \operatorname{reltype}({\mathcal R}(I))\). Moreover they study equimultiple ideals of deviation \(1\), that is, ideals \(I\) such that height\((I)\) is equal to the analytic spread \(\ell\) of \(I\), and \(I\) is generated by \(\ell+1\) elements. They give a sufficient condition on the ideals in this class, to have \(\operatorname{reltype}(F(I)) = \operatorname{reltype}({\mathcal R}(I))\).
reviewed by: Emanuela De Negri
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 6496847
zbMATH Keywords: fiber cone
zbMATH Keywords: Rees algebra
zbMATH Keywords: relation type
zbMATH Keywords: lexsegment ideal
MaRDI profile type: Publication
full work available at URL: s40306-015-0142-z
OpenAlex ID: W922352950
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DOI: 10.1007/S40306-015-0142-Z
description: scientific article; zbMATH DE number 6496847