{"paper":{"title":"On the Betti numbers, Poincar\\'e polynomials, and Euler characteristics of $\\overline{\\mathcal M}_{0,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.AG","authors_text":"Giordano Cotti","submitted_at":"2026-07-29T10:51:34Z","abstract_excerpt":"In this paper, we revisit the Poincar\\'e polynomials, Betti numbers, and Euler characteristics of the Deligne-Mumford moduli spaces $\\overline{\\mathcal M}_{0,n}$ of stable $n$-pointed rational curves. We give elementary derivations of two recent closed formulas for their Poincar\\'e polynomials, due respectively to Aluffi-Marcolli-Nascimento (arXiv:2406.13095) and to Eur-Ferroni-Matherne-Pagaria-Vecchi (arXiv:2504.16776). Our approach shows that both formulas are already implicit in the generating-series results of Getzler and Manin, and can be extracted from them by elementary manipulations of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26755","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26755/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}