CHOW QUOTIENTS AND PROJECTIVE BUNDLE FORMULAS FOR EULER-CHOW SERIES

Given a projective algebraic variety X, let IIp (X) denote the monoid of effective algebraic equivalence classes of effective algebraic cycl es on X. The p-th Euler-Chow series of X is an element in the formal m onoid-ring Z[IIp (X)] defined in terms of Euler characteristics of the Chow varieties C-p, alpha (X) of X, with alpha epsilon IIp (X). We pr ovide a systematic treatment of such series, and give projective bundl e formulas which generalize previous results by [LY87] and [Eli94]. Th e techniques used involve the Chow quotients introduced in [KSZ91], an d this allows the computation of various examples including some Grass mannians and flag varieties. There are relations between these example s and representation theory, and further results point to interesting connections between Euler-Chow series for certain varieties and the to pology of the moduli spaces (M) over bar(0 n+1).