Chow coordinates

In mathematics, and more particularly in the field of algebraic geometry, Chow coordinates are a generalization of Plücker coordinates, applying to non-linear m -dimensional algebraic varieties of degree d in Pn , that is, n -dimensional projective space. They are named for W. L. Chow.

To define the Chow coordinates, take the intersection of an algebraic variety Z of degree d by linear subspaces U of appropriate Codimension. 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.