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.
