Rational normal curve

In mathematics, the rational normal curve is a smooth, rational curve $C$ of degree $n$ in projective n-space $P$ . 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 flat 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.

单词	Rational normal curve
释义	Rational normal curve 英语百科 Rational normal curve In mathematics, the rational normal curve is a smooth, rational curve $C$ of degree $n$ in projective n-space $P$ . 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 flat 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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