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

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

2007-02-16

arxiv.org/abs/math/0702472v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $A$.

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