Similar ideas are to be associated with the concept of a curve. A space curve can be parametrized by a map from a variety of 1 dimension into a position vector of 3 dimensions. Dually, a curve may be defined by the intersection of two implicit surfaces. The ideas need to be abstracted to varieties of larger dimensions. Not every curve can be represented by a single parametrization. A particular problem occurs when a curve is formed by the cuspoidal contact of two surfaces.

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