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Recursive algorithm and log-concavity of representations on the cohomology of overline{mathcal M}_(0,n)
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Recursive algorithm and log-concavity of representations on the cohomology of overline{mathcal M}_(0,n)
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We provide a programmable recursive algorithm for the $\mathbb{S}_n$-representations on the cohomology of the moduli spaces $\overline{\mathcal M}_{0,n}$ of $n$-pointed stable curves of genus 0. As an application, we find explicit inductive and asymptotic formulas for the invariant part $H^*(\overline{\mathcal M}_{0,n}/\mathbb{S}_n)$ and prove that its Poincar\'e polynomial is asymptotically log-concave. Based on numerical computations with our algorithm, we further conjecture that the sequence $\{H^{2k}(\overline{\mathcal M}_{0,n})\}$ of $\mathbb{S}_n$-modules is equivariantly log-concave.
Forward citations
Cited by 2 Pith papers
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Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof
Proves real-rootedness and ultra-log-concavity of Poincaré polynomials for moduli spaces of rational curves via a bivariate deformation and Sturm-Rolle argument in an AI-assisted workflow.
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Asymptotic distribution of the Betti numbers of $\overline{\mathcal{M}}_{0,n}$
Betti numbers of the moduli space of rational curves with n marked points and the Fulton-MacPherson configuration space are asymptotically normally distributed.
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