Cohomological amplitude for constructible sheaves on moduli spaces of\n curves

2012/03/20 by Eduard Looijenga, Looijenga, Eduard
Computer Science · Mathematics · #14B15 #14F05 #14H10 #32G15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1203.4548

openalex publication_date 2012/03/20 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We give bounds for the cohomology of constructible sheaves on the moduli\nstacks M_g,n over the complex field. This enables us recover Harer's bound\nfor the virtual cohomological dimension of the associated mapping class groups\nas well the theorem of Diaz on complete subvarieties of M_g. We also obtain\nsuch bounds for any open subset of the Deligne-Mumford compactification of\nM_g,n that is a union of strata. Our proof yields a template for obtaining\nsimilar bounds for the cohomological dimension for quasicoherent sheaves on\nM_g,n.\n

Citations

• An affine open covering of M_g for g ≤ 5

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