Chow groups of the moduli spaces of weighted pointed stable curves of genus zero

Abstract

The moduli space ${\bar{M}}_A$ of weighted pointed stable curves of genus zero is stratified according to the degeneration types of such curves. We show that the homology groups of the moduli space ${\bar{M}}_A$ are generated by the strata of ${\bar{M}}_A$ and give all additive relations between them. We also observe that the Chow groups $A_i{\bar{M}}_A$ and the homology groups $H_{2i}{\bar{M}}_A$ are isomorphic. This generalizes Kontsevich-Manin's and Losev-Manin's theorems to arbitrary weight data $A$.

Final version (to appear in Advances in Math), 20 pages, 1 figure