We compute the Chow groups and Fulton–MacPherson’s operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary ...

Given a projective algebraic variety X, let p(X) denote the monoid of eeective algebraic equivalence classes of eeective algebraic cycles on X. The p-th Euler-Chow series of X is an element in the formal monoid-ring Z p(X)] ] deened in terms of Euler characteristics of the Chow varieties Cp;; (X) of X, with 2 p(X). We provide a systematic treatment of such series, and give projective bundle for...