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In mathematics, the rational normal curve is a smooth, rational curve of degree in projective n-space . It is a simple example of a projective variety; formally, it is the Veronese variety when the domain is the projective line. For it is the flat conic and for it is the twisted cubic. The term "normal" is an old term meaning that the linear system defining the embedding is complete (and has nothing to do with normal schemes). The intersection of the rational normal curve with an affine space is called the moment curve. ==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 of these to specify the curve. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「rational normal curve」の詳細全文を読む スポンサード リンク
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