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 formulas which generalize previous results by LY87] and Eli94]. The techniques used involve the Chow quotients introduced in KSZ91], and this allows the computation of various examples including some Grassmannians and ag varieties. There are relations between these examples and representation theory, and further results point to interesting connections between Euler-Chow series for certain varieties and the topology of the moduli spaces M0;n+1.