Cohomological amplitude for constructible sheaves on moduli spaces of curves
Algebraic Geometry
2013-09-02 v4
Abstract
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}.
Keywords
Cite
@article{arxiv.1203.4548,
title = {Cohomological amplitude for constructible sheaves on moduli spaces of curves},
author = {Eduard Looijenga},
journal= {arXiv preprint arXiv:1203.4548},
year = {2013}
}
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This paper is withdrawn because the proof of the main result is incomplete.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