{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-serre-spectral-sequence-for-the-moduli","title":"A Serre spectral sequence for the moduli space of tropical curves","arxiv_id":"2307.01960","date":"2023-07-04","proceeding":null,"authors":["Christin Bibby","Melody Chan","Nir Gadish","Claudia He Yun"],"abstract":"We construct, for all $g\\geq 2$ and $n\\geq 0$, a spectral sequence of rational $S_n$-representations which computes the $S_n$-equivariant reduced rational cohomology of the tropical moduli spaces of curves $\\Delta_{g,n}$ in terms of compactly supported cohomology groups of configuration spaces of $n$ points on graphs of genus $g$. Using the canonical $S_n$-equivariant isomorphisms $\\widetilde{H}^{i-1}(\\Delta_{g,n};\\mathbb{Q}) \\cong W_0 H^i_c(\\mathcal{M}_{g,n};\\mathbb{Q})$, we calculate the weight $0$, compactly supported rational cohomology of the moduli spaces $\\mathcal{M}_{g,n}$ in the range $g=3$ and $n\\leq 9$, with partial computations available for $n\\leq 13$.","url_abs":"https://arxiv.org/abs/2307.01960v2","url_pdf":"https://arxiv.org/pdf/2307.01960v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-serre-spectral-sequence-for-the-moduli","repo_url":"https://github.com/claudiaheyun/bcgy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}