Cayley-Bacharach theorem of piecewise algebraic curves.
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.
scientific article; zbMATH DE number 2055554