Implicitization of rational ruled surfaces with $μ$-bases

Details Implicitization of rational ruled surfaces with $μ$-bases Implicitization of rational ruled surfaces with $μ$-bases

2007-02-22

arxiv.org/abs/math/0702658v2

Mathematics

Algebraic Geometry

Scientific paper

Chen, Sederberg, and Zheng introduced the notion of a $\mu$-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization. We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces.

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