Rational cohomology of the moduli spaces of pointed genus 1 curves

We give a combinatorial description of the rational cohomology of the moduli spaces of pointed genus 1 curves with \(n\) marked points and level \(N\) structures. More precisely, we explicitly describe the \(E_2\) term of the Leray spectral sequence of the forgetful mapping \(\EuScript{M}_{1,n}(N)\t...

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Bibliographic Details
Published in:arXiv.org 2013-03
Main Author: Gorinov, Alexey G
Format: Article
Language:English
Subjects:
Combinatorial analysis
Homology
Mapping
Online Access:Get full text
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Summary:We give a combinatorial description of the rational cohomology of the moduli spaces of pointed genus 1 curves with \(n\) marked points and level \(N\) structures. More precisely, we explicitly describe the \(E_2\) term of the Leray spectral sequence of the forgetful mapping \(\EuScript{M}_{1,n}(N)\to\EuScript{M}_{1,1}(N)\) and show that the result is isomorphic to the rational cohomology of \(\EuScript{M}_{1,n}(N)\) as a rational mixed Hodge structure equipped with an action of the symmetric group \(\mathfrak{S}_n\). The classical moduli space \(\EuScript{M}_{1,n}\) is the particular case N=1.
ISSN:2331-8422