Rational cohomology of the moduli spaces of pointed genus 1 curves

2013/03/22 by A. G. Gorinov, Gorinov, Alexey G.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1303.5693

openalex publication_date 2013/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 E₂ term of the Leray spectral sequence of the forgetful mapping \EuScriptM_1,n(N)→\EuScriptM_1,1(N) and show that the result is isomorphic to the rational cohomology of \EuScriptM_1,n(N) as a rational mixed Hodge structure equipped with an action of the symmetric group \mathfrakS_n. The classical moduli space \EuScriptM_1,n is the particular case N=1.

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