Eduard Looijenga
Published 2012-03-20, updated 2013-08-30Version 4
We give bounds for the cohomology of constructible sheaves on the moduli stacks M_{g,n} over the complex field. This enables us recover Harer's bound for the virtual cohomological dimension of the associated mapping class groups as well the theorem of Diaz on complete subvarieties of M_g. We also obtain such bounds for any open subset of the Deligne-Mumford compactification of M_{g,n} that is a union of strata. Our proof yields a template for obtaining similar bounds for the cohomological dimension for quasicoherent sheaves on M_{g,n}.
Comments: This paper is withdrawn because the proof of the main result is incomplete. This is due to an incorrect use of 1.8 in the proof of 3.1
Cohomology of moduli spaces
On the rationality of moduli spaces of pointed curves
The rationality of the moduli spaces of trigonal curves
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