Journal of Algebraic Geometry CHOW QUOTIENTS AND PROJECTIVE BUNDLE FORMULAS FOR EULER-CHOW SERIES

Abstract. Given a projective algebraic variety X, let p(X) denote the monoid of eective alge-braic equivalence classes of eective algebraic cycles on X. The p-th Euler-Chow series of X is an element in the formal monoid-ring Z[[p(X)]] dened 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 vari-ous examples including some Grassmannians and flag 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