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Rational cohomology of the moduli spaces of pointed genus 1 curves (1303.5693v1)
Published 22 Mar 2013 in math.AG
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 $E_2$ 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.