Cayley-Bacharach theorem of piecewise algebraic curves.
type: Item
instance of: scholarly article
title: Cayley-Bacharach theorem of piecewise algebraic curves.
zbMATH Open document ID: 1070.14034
published in: Journal of Computational and Applied Mathematics
publication date: 2004-03-14T00:00:00Z
review text: A piecewise algebraic curve is a generalization of the classical algebraic curve. The piecewise algebraic curve is not only important for the interpolation by bivariate splines but also a useful tool for studying traditional algebraic curves. It is well known that the Cayley-Bacharach theorem is an important and classical result in algebraic geometry. This result has been successively generalized, improved and reinterpreted, and this development continues today [see for instance the paper by \textit{S.-L. Tan}, J. Algebr. Geom. 9, No.~2, 201--222 (2000; Zbl 0953.14033)]. In this paper, by using Bézout's theorem and a Noether-type theorem of piecewise algebraic curves, the Cayley-Bacharach theorem and Hilbert function of \(C^0\) piecewise algebraic curves are presented.
reviewed by: J. Rafael Sendra
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 2055554
zbMATH Keywords: bivariate spline functions
zbMATH Keywords: piecewise algebraic curves
zbMATH Keywords: Cayley-Bacharach theorem
zbMATH Keywords: Bézout's theorem
author: Ren-Hong Wang
author: Chun-Gang Zhu
MaRDI profile type: Publication
full work available at URL: j.cam.2003.08.072
OpenAlex ID: W2060201773
cites work: Cayley-Bacharach theorems and conjectures
cites work: Q4143433
cites work: The Bézout number for piecewise algebraic curves
cites work: Q4946475
cites work: Q5799167
cites work: Q4130491
cites work: Multivariate spline and algebraic geometry
cites work: Q4530239
cites work: Piecewise algebraic curve
cites work: Q4703998
cites work: Nöther-type theorem of piecewise algebraic curves
DOI: 10.1016/J.CAM.2003.08.072
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description: scientific article; zbMATH DE number 2055554