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**Nöther-type theorem of piecewise algebraic curves on quasi-cross-cut partition.**
*(English)*
Zbl 1177.14076

Summary: Nöther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nöther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nöther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.

### MSC:

14H99 | Curves in algebraic geometry |

65D07 | Numerical computation using splines |

65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |

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\textit{C. Zhu} and \textit{R. Wang}, Sci. China, Ser. A 52, No. 4, 701--708 (2009; Zbl 1177.14076)

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### References:

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