{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6PLJPFK4V2P6ITXUDQCAVUJEXH","short_pith_number":"pith:6PLJPFK4","schema_version":"1.0","canonical_sha256":"f3d697955cae9fe44ef41c040ad124b9d8f3cf24d8f81b8c0ed62a88296d761e","source":{"kind":"arxiv","id":"1009.0184","version":4},"attestation_state":"computed","paper":{"title":"The universal theta divisor over the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Gavril Farkas","submitted_at":"2010-09-01T14:23:12Z","abstract_excerpt":"We carry out a complete birational classification of the universal theta divisor Th_g over the moduli space of curves of genus g, and show that Th_g enjoys good rationality properties for g<12, and is a variety of general type for g\\geq 12. The key ingredient is an intersection-theoretic study of the universal antiramification locus of the Gauss map. We also present a complete classification of the universal symmetric product of degree g-2 over M_g."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.0184","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-01T14:23:12Z","cross_cats_sorted":[],"title_canon_sha256":"d2d7d1f58c64289d660b15453dd453384ffc7c64fd541dd0a3345420866f08bf","abstract_canon_sha256":"81c9905314cf0da7bcdb25ba75c7ad7a47e697328ee3217f080ebb139ce1b036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.729935Z","signature_b64":"YFHngVgGUfbl8Kr5MBk2TbYqfN3AwcN+Y2SfH5CIyUsImTAXntpWaJR8niltGghNX+9AJjtMStVQyLrsdHxpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3d697955cae9fe44ef41c040ad124b9d8f3cf24d8f81b8c0ed62a88296d761e","last_reissued_at":"2026-05-18T00:57:38.729447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.729447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The universal theta divisor over the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Gavril Farkas","submitted_at":"2010-09-01T14:23:12Z","abstract_excerpt":"We carry out a complete birational classification of the universal theta divisor Th_g over the moduli space of curves of genus g, and show that Th_g enjoys good rationality properties for g<12, and is a variety of general type for g\\geq 12. The key ingredient is an intersection-theoretic study of the universal antiramification locus of the Gauss map. We also present a complete classification of the universal symmetric product of degree g-2 over M_g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0184","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.0184","created_at":"2026-05-18T00:57:38.729518+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.0184v4","created_at":"2026-05-18T00:57:38.729518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0184","created_at":"2026-05-18T00:57:38.729518+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PLJPFK4V2P6","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PLJPFK4V2P6ITXU","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PLJPFK4","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH","json":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH.json","graph_json":"https://pith.science/api/pith-number/6PLJPFK4V2P6ITXUDQCAVUJEXH/graph.json","events_json":"https://pith.science/api/pith-number/6PLJPFK4V2P6ITXUDQCAVUJEXH/events.json","paper":"https://pith.science/paper/6PLJPFK4"},"agent_actions":{"view_html":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH","download_json":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH.json","view_paper":"https://pith.science/paper/6PLJPFK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.0184&json=true","fetch_graph":"https://pith.science/api/pith-number/6PLJPFK4V2P6ITXUDQCAVUJEXH/graph.json","fetch_events":"https://pith.science/api/pith-number/6PLJPFK4V2P6ITXUDQCAVUJEXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH/action/storage_attestation","attest_author":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH/action/author_attestation","sign_citation":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH/action/citation_signature","submit_replication":"https://pith.science/pith/6PLJPFK4V2P6ITXUDQCAVUJEXH/action/replication_record"}},"created_at":"2026-05-18T00:57:38.729518+00:00","updated_at":"2026-05-18T00:57:38.729518+00:00"}