Chow variety
In mathematics, particularly in the field of algebraic geometry, a Chow variety is an algebraic variety whose points correspond to effective algebraic cycles of fixed dimension and degree on a given projective space. More precisely, the Chow variety Gr ( k , d , n ) {\displaystyle \operatorname {Gr} (k,d,n)} is the fine moduli variety parametrizing all effective algebraic cycles of dimension k − 1 {\displaystyle k-1} and degree d {\displaystyle d} in P n − 1 {\displaystyle \mathbb {P} ^{n-1}} .