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 Variety## Explore 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 Coordinates## Cite this as:

Weisstein, Eric W. "Chow Coordinates."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ChowCoordinates.html