Rational normal curve

In mathematics, the rational normal curve is a smooth, rational curve $C$ of degree $n$ in projective n-space $P n$ . It is a simple example of a projective variety; formally, it is the Veronese variety when the domain is the projective line. For $n = 2$ it is the plane conic $Z 0 Z 2 = Z 21,$ and for $n = 3$ it is the twisted cubic. The term "normal" refers to projective normality, not normal schemes. The intersection of the rational normal curve with an affine space is called the moment curve.

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