Plücker coordinates [SEP] named after
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P. Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P and points on a quadric in P (projective 5-space). A predecessor and special case of Grassmann coordinates (which describe "k"-dimensional linear subspaces, or "flats", in an "n"-dimensional Euclidean space), Plücker
Chow variety
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 formula_1, that is, "n"-dimensional projective space. They are named for Wei-Liang 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"