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In mathematics, and more particularly in the field of algebraic geometry, Chow coordinates are a generalization of Plücker coordinates, applying to ''m''-dimensional algebraic varieties of degree ''d'' in ''Pn'', that is, ''n''-dimensional projective space. They are named for W. L. Chow. A Chow variety is a variety whose points correspond to all cycles of a given projective space of given dimension and degree. ==Definition== To define the Chow coordinates, take the intersection of an algebraic variety ''Z'' of degree ''d'' and dimension ''m'' by linear subspaces ''U'' of codimension ''m''. When ''U'' is in general position, the intersection will be a finite set of ''d'' distinct points. Then the coordinates of the ''d'' points of intersection are algebraic functions of the Plücker coordinates of U, and by taking a symmetric function of the algebraic functions, a homogeneous polynomial known as the Chow form (or Cayley form) of Z is obtained. The Chow coordinates are then the coefficients of the Chow form. Chow coordinates can generate the smallest field of definition of a divisor. The Chow coordinates define a point in the projective space corresponding to all forms. 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「Chow coordinates」の詳細全文を読む スポンサード リンク
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