Definition
The rational normal curve may be given parametrically as the image of the map
which assigns to the homogeneous coordinates the value
In the affine coordinates of the chart the map is simply
That is, the rational normal curve is the closure by a single point at infinity of the affine curve .
Equivalently, rational normal curve may be understood to be a projective variety, defined as the common zero locus of the homogeneous polynomials
where are the homogeneous coordinates on . The full set of these polynomials is not needed; it is sufficient to pick n of these to specify the curve.
Read more about this topic: Rational Normal Curve
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