Rational Normal Curve
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space mathbb{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 standard parabola y = x2, and for n=3 it is the twisted cubic.The rational normal curve may be given parametrically as the image of the map nu:mathbb{P}^1tomathbb{P}^n which assigns to the homogeneous…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space mathbb{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 standard parabola y = x2, and for n=3 it is the twisted cubic.The rational normal curve may be given parametrically as the image of the map nu:mathbb{P}^1tomathbb{P}^n which assigns to the homogeneous coordinates [S:T] the value nu:[S:T] mapsto [S^n:S^{n-1}T:S^{n-2}T^2:ldots:T^n]. In the affine coordinates of the chart x_0neq0 the map is simply nu:x mapsto (x,x^2, ldots ,x^n).