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In mathematics, a Hessian pair or Hessian duad, named for Otto Hesse, is a pair of points of the projective line canonically associated with a set of 3 points of the projective line. More generally, one can define the Hessian pair of any triple of elements from a set that can be identified with a projective line, such as a rational curve, a pencil of divisors, a pencil of lines, and so on. ==Definition== If is a set of 3 distinct points of the projective line, then the Hessian pair is a set of two points that can be defined by any of the following properties: *''P'' and ''Q'' are the roots of the Hessian of the binary cubic form with roots ''A'', ''B'', ''C''. *''P'' and ''Q'' are the two points fixed by the unique projective transformation taking ''A'' to ''B'', ''B'' to ''C'', and ''C'' to ''A''. *''P'' and ''Q'' are the two points that when added to ''A'', ''B'', ''C'' form an equianharmonic set (a set of 4 points with cross-ratio a cube root of 1). *''P'' and ''Q'' are the images of 0 and ∞ under the projective transformation taking the three cube roots of 1 to ''A'', ''B'', ''C''. 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「Hessian pair」の詳細全文を読む スポンサード リンク
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