specified using the parametric representation, by arranging of the points to lie on the coordinate axes, and then mapping the other two points to and . The tangent and secant lines of a rational normal curve are pairwise disjoint, except at points of the curve itself. This is a property shared by sufficiently positive embeddings of any projective variety. There are independent quadrics that generate the ideal of the curve. The curve is not a complete intersection, for . That is, it cannot be defined (as a subscheme of projective space) by only equations, that being the codimension of the curve in . The canonical mapping for a hyperelliptic curve has image a rational normal curve, and is 2-to-1. Every irreducible non-degenerate curve of degree is a rational normal curve. See also Rational normal scroll References Joe Harris, Algebraic Geometry, A First Course, (1992) Springer-Verlag, New York. Algebraic curves Birational geometry