An orbifold partition of ${\overline{M}_g^n}$
Abstract
Description
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.
16 pages, Latex Version 2.09, will appear in The Moduli space of Curves (eds. Dijkgraaf, Faber, van der Geer), Progress in Math., Birkh"auser
16 pages, Latex Version 2.09, will appear in The Moduli space of Curves (eds. Dijkgraaf, Faber, van der Geer), Progress in Math., Birkh"auser