{"paper":{"title":"The Kodaira classification of the moduli space of pointed curves in genus $3$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ruben de Preter","submitted_at":"2025-06-30T13:01:08Z","abstract_excerpt":"We complete the Kodaira classification of the moduli spaces $\\overline{\\mathcal{M}}_{g,n}$ of curves with marked points in genus $g=3$, by proving that $\\overline{\\mathcal{M}}_{3,n}$ is of general type for $n \\geq 15$. We prove that the singularities of $\\overline{\\mathcal{M}}_{3,n}$ impose no adjunction conditions for $n \\geq 1$ and that the canonical class of $\\overline{\\mathcal{M}}_{3,n}$ is big for $n \\geq 15$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23812","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/2506.23812/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"}