A generalization of Grassmann coordinates to 
-D
algebraic varieties of degree 
in 
, where 
is an 
-dimensional projective space. To define the Chow coordinates,
take the intersection of an 
-D algebraic variety 
of degree 
by an 
-D subspace 
of 
. Then the coordinates of the 
points of intersection are algebraic functions of the Grassmann
coordinates of 
,
and by taking a symmetric function of the algebraic functions, a homogeneous
polynomial known as the Chow form of 
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.
Chow Coordinates
See also
Chow Ring, Chow VarietyExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Chow CoordinatesCite this as:
Weisstein, Eric W. "Chow Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChowCoordinates.html