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Cayley-Bacharach theorem of piecewise algebraic curves. (English) Zbl 1070.14034
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 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.

##### MSC:
 14H50 Plane and space curves 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 65D07 Numerical computation using splines 13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
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##### References:
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