Real algebraic curves as complete intersections
type: Item
instance of: scholarly article
title: Real algebraic curves as complete intersections
zbMATH Open document ID: 0595.14036
DOI: 10.1007/BF01161973
author: Wojciech Kucharz
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173832
review text: It is known that for each \(n\geq 3\) there exists a nonsingular algebraic curve C in \({\mathbb{R}}^ n\) such that the ideal \(I_ p(C)\) of \({\mathbb{R}}[x_ 1,...,x_ n]\) of polynomials vanishing on C cannot be generated by n-1 elements. Let \(O({\mathbb{R}}^ n)\) be the ring of regular functions on \({\mathbb{R}}^ n\). The ring \(O({\mathbb{R}}^ n)\) is naturally isomorphic to the localization of \({\mathbb{R}}[x_ 1,...,x_ n]\) with respect to the multiplicatively closed subset consisting of polynomials which do not vanish on \({\mathbb{R}}^ n\). It is shown in the paper that for any nonsingular algebraic curve C in \({\mathbb{R}}^ n\), the ideal I(C) of \(O({\mathbb{R}}^ n)\) of regular functions vanishing on C can be generated by n-1 elements.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 3957307
zbMATH Keywords: real algebraic curves as complete intersections
MaRDI profile type: Publication
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OpenAlex ID: W3015265474
description: scientific article; zbMATH DE number 3957307