{"paper":{"title":"Rational curves on cubic hypersurfaces in positive characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The Kontsevich moduli space of stable maps to a smooth cubic hypersurface is irreducible for dimension at least 4.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Natsume Kitagawa","submitted_at":"2026-04-29T11:43:47Z","abstract_excerpt":"We study the moduli spaces of rational curves on cubic hypersurfaces in characteristic $\\neq2,3$. As a result, we prove that for every integer $d\\geq1$ the Kontsevich moduli space of stable maps on a smooth cubic hypersurface $X$ of degree $d$ is irreducible if the dimension of $X$ is greater than or equal to $4$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove that for every integer d≥1 the Kontsevich moduli space of stable maps on a smooth cubic hypersurface X of degree d is irreducible if the dimension of X is greater than or equal to 4.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The hypersurface is smooth and the characteristic is not 2 or 3; the proof likely relies on these to avoid singularities and characteristic-dependent degenerations in the moduli space construction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The Kontsevich moduli space of stable maps to a smooth cubic hypersurface of dimension at least 4 is irreducible for any degree d in characteristic not 2 or 3.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Kontsevich moduli space of stable maps to a smooth cubic hypersurface is irreducible for dimension at least 4.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1d73fb3154cb8018e902c817c839fb9679d1fd2be94249d075faab593c948302"},"source":{"id":"2604.26556","kind":"arxiv","version":2},"verdict":{"id":"10460f57-8e78-46a1-90ac-97254ae4aa7a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:40:33.101659Z","strongest_claim":"we prove that for every integer d≥1 the Kontsevich moduli space of stable maps on a smooth cubic hypersurface X of degree d is irreducible if the dimension of X is greater than or equal to 4.","one_line_summary":"The Kontsevich moduli space of stable maps to a smooth cubic hypersurface of dimension at least 4 is irreducible for any degree d in characteristic not 2 or 3.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The hypersurface is smooth and the characteristic is not 2 or 3; the proof likely relies on these to avoid singularities and characteristic-dependent degenerations in the moduli space construction.","pith_extraction_headline":"The Kontsevich moduli space of stable maps to a smooth cubic hypersurface is irreducible for dimension at least 4."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26556/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:48:54.729164Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:02:43.479207Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c1323353810852ea7527b107766f465a39c053d380cbd90fbd6dd8a539d99708"},"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"}