An orbifold partition of ${\overline{M}_g^n}$

Details An orbifold partition of ${\overline{M}_g^n}$ An orbifold partition of ${\overline{M}_g^n}$

1995-03-27

arxiv.org/abs/alg-geom/9503019v1

Mathematics

Algebraic Geometry

16 pages, Latex Version 2.09, will appear in The Moduli space of Curves (eds. Dijkgraaf, Faber, van der Geer), Progress in Mat

Scientific paper

We define a partition of ${\overline{M}_g^n}$ and show that the cohomology of ${\overline{M}_g^n}$ in a given degree admits a filtration whose respective quotients are isomorphic to the shifted cohomology groups of the parts if $g$ is sufficiently large. This implies that the map $H^k({\overline{M}_g^n}) \ra H^k(M_g^n)$ is onto and that the Hodge structure of $H^k(M_g^n)$ is pure of weight $k$ if $g \geq 2k+1$. Our main ingredient is the stability theorem of Harer and Ivanov.

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