{"paper":{"title":"Equivariant Euler characteristics of $\\overline{\\mathscr{M}}_{g, n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Adrian Diaconu","submitted_at":"2018-03-22T13:38:06Z","abstract_excerpt":"Let $\\overline{\\mathscr{M}}_{g, n}$ be the moduli space of $n$-pointed stable genus $g$ curves, and let $\\mathscr{M}_{g, n}$ be the moduli space of $n$-pointed smooth curves of genus $g.$ In this paper, we obtain an asymptotic expansion for the characteristic of the free modular operad $\\mathbb{M}\\mathcal{V}$ generated by a stable $\\mathbb{S}$-module $\\mathcal{V},$ allowing to effectively compute $\\mathbb{S}_{n}$-equivariant Euler characteristics of $\\overline{\\mathscr{M}}_{g, n}$ in terms of $\\mathbb{S}_{n'}$-equivariant Euler characteristics of $\\mathscr{M}_{g'\\!, n'}$ with $0\\le g' \\le g,$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08349","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":""},"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"}