Cayley–Bacharach theorem of piecewise algebraic curves

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摘要

The piecewise algebraic curve, determined by a bivariate spline function, is a generalization of the classical algebraic curve. In this paper, by using Bezout's theorem and Nöther-type theorem of piecewise algebraic curves, the Cayley–Bacharach theorem and Hilbert function of C0 piecewise algebraic curves are presented.

论文关键词：Bivariate splines,Piecewise algebraic curves,Cayley–Bacharach theorem,Nöther-type theorem,Bezout's theorem

论文评审过程：Received 1 October 2002, Revised 5 June 2003, Available online 1 December 2003.

论文官网地址：https://doi.org/10.1016/j.cam.2003.08.072