On complete intersection real curves
type: Item
instance of: scholarly article
title: On complete intersection real curves
zbMATH Open document ID: 0577.14017
DOI: 10.1216/RMJ-1984-14-4-919
published in: Rocky Mountain Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let C be a curve over \({\mathbb{R}}\) in the sense of \textit{A. Tognoli} [''Algebraic geometry and Nash functions'' (1978; Zbl 0418.14002)]. In this report the following problem is studied: Does there exist an embedding \(\phi\) : \(C\to {\mathbb{R}}^ n\) satisfying (i) \(\Gamma\) (C,\({\mathcal O}_ C)\cong N^{-1}{\mathbb{R}}[\phi (C)]\), where \(N=\{s\in {\mathbb{R}}[\phi (C)]| s(x)\neq 0\forall x\in \phi (C)\}.\) (ii) \({\mathbb{R}}[\phi (C)]\) is an abstract complete intersection. The results are related to Kumar's work on complete intersections in the case of finitely generated algebras over a field [\textit{N. M. Kumar}, J. Math. Kyoto Univ. 17, 533-538 (1977; Zbl 0384.14016)].
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 3922840
zbMATH Keywords: real curves
zbMATH Keywords: embedding
zbMATH Keywords: complete intersection
author: Maria Grazia Marinari
author: Mario Raimondo
MaRDI profile type: Publication
full work available at URL: rmj-1984-14-4-919
OpenAlex ID: W2047400065
description: scientific article; zbMATH DE number 3922840