Reply to KD Hall and CC Chow

Chow Groups, Chow Cohomology, and Linear Varieties

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 ...

Chow Quotients and Euler - Chow Series

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...

Chow Quotients and Projective Bundle Formulas for Euler-chow Series

Given a projective algebraic variety X, let Πp(X) denote the monoid of effective algebraic equivalence classes of effective algebraic cycles on X. The p-th Euler-Chow series of X is an element in the formal monoid-ring Z[[Πp(X)]] defined in terms of Euler characteristics of the Chow varieties Cp,α (X) of X, with α ∈ Πp(X). We provide a systematic treatment of such series, and give projective bu...

The Authors’ Reply

Chow Polylogarithms and Regulators

where r denotes the cross-ratio. In this note we show that the Bloch-Wigner function can be naturally extended to the (infinite dimensional) variety of all algebraic curves in CP 3 which are in sufficiently general position with respect to a given simplex L. (By definition a simplex in CP 3 is a collection of 4 hyperplanes in generic position). We call the corresponding function the Chow diloga...