{"paper":{"title":"The unirationality of $S_9^-$ and moduli spaces of pointed spin curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The moduli space of odd spin curves of genus 9 is unirational.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Gavril Farkas","submitted_at":"2026-04-20T18:18:43Z","abstract_excerpt":"We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known. This is achieved by realizing birationally the moduli space of odd spin curves of genus g<10 as a locally trivial projective bundle over a certain (finite quotient of the) moduli space of n-pointed odd stable spin curves of genus g'<g. We then present general results on the Kodaira dimension of both components of the moduli spaces of n-pointed spin curves of genus g."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The birational realization of the moduli space of odd spin curves of genus g<10 as a locally trivial projective bundle over a finite quotient of the moduli space of n-pointed odd stable spin curves of genus g'<g is valid.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The moduli space of odd spin curves of genus 9 is unirational.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The moduli space of odd spin curves of genus 9 is unirational.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"360739df74040fe22f6a557a81b012b13b159ac41d367af117885f2168c1300f"},"source":{"id":"2604.18719","kind":"arxiv","version":2},"verdict":{"id":"8eb09d55-f6e7-430a-9962-3cf54bf58afe","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T03:26:28.289277Z","strongest_claim":"We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known.","one_line_summary":"The moduli space of odd spin curves of genus 9 is unirational.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The birational realization of the moduli space of odd spin curves of genus g<10 as a locally trivial projective bundle over a finite quotient of the moduli space of n-pointed odd stable spin curves of genus g'<g is valid.","pith_extraction_headline":"The moduli space of odd spin curves of genus 9 is unirational."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.18719/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"}