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 coordinat...
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).
