Recursive algorithm and log-concavity of representations on the cohomology of $\overline{\mathcal M}_{0,n}$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929466020724736 |
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| author | Choi, Jinwon Kiem, Young-Hoon Lee, Donggun |
| author_facet | Choi, Jinwon Kiem, Young-Hoon Lee, Donggun |
| contents | 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 Poincaré 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursive algorithm and log-concavity of representations on the cohomology of $\overline{\mathcal M}_{0,n}$ Choi, Jinwon Kiem, Young-Hoon Lee, Donggun Algebraic Geometry Combinatorics Representation Theory 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 Poincaré 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. |
| title | Recursive algorithm and log-concavity of representations on the cohomology of $\overline{\mathcal M}_{0,n}$ |
| topic | Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2408.10728 |