Chow Coordinates

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take the intersection of an m-D algebraic variety Z of degree d by an (n-m)-D subspace U of P^n. Then the coordinates of the d points of intersection are algebraic functions of the Grassmann coordinates of U, and by taking a symmetric function of the algebraic functions, a homogeneous polynomial known as the Chow 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.

See also

Chow Ring, Chow Variety

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Chow, W.-L. and van der Waerden., B. L. "Zur algebraische Geometrie IX." Math. Ann. 113, 692-704, 1937.Wilson, W. S.; Chern, S. S.; Abhyankar, S. S.; Lang, S.; and Igusa, J.-I. "Wei-Liang Chow." Not. Amer. Math. Soc. 43, 1117-1124, 1996.

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Chow Coordinates

Cite this as:

Weisstein, Eric W. "Chow Coordinates." From MathWorld--A Wolfram Web Resource.

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