{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7FRC5NCJLQPZA6QXI6TUILZ467","short_pith_number":"pith:7FRC5NCJ","schema_version":"1.0","canonical_sha256":"f9622eb4495c1f907a1747a7442f3cf7c5dcc104793246304925dc8a104888d8","source":{"kind":"arxiv","id":"1106.1006","version":6},"attestation_state":"computed","paper":{"title":"Unirationality of Hurwitz spaces of coverings of degree <= 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vassil Kanev","submitted_at":"2011-06-06T10:21:19Z","abstract_excerpt":"Let $Y$ be a smooth, projective curve of genus $g\\geq 1$ over the complex numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings $p:X \\to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy group equal to $S_d$, and $det(p_{*}O_X/O_Y)$ isomorphic to a fixed line bundle $A^{-1}$ of degree $-e$. We prove that, when $d=3, 4$ or $5$ and $n$ is sufficiently large (precise bounds are given), these Hurwitz spaces are unirational. If in addition $(e,2)=1$ (when $d=3$), $(e,6)=1$ (when $d=4$) and $(e,10)=1$ (when $d=5$), then these Hurwitz spaces are rational."},"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":"1106.1006","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-06T10:21:19Z","cross_cats_sorted":[],"title_canon_sha256":"d81667d9988b342e974d2b2159418e6eebbaa4c4f8930778894ce7a9e4df7d3d","abstract_canon_sha256":"b8513c5612d8b14722333b7f3018d2942dedd28dd51bc444b30c8e2b3fbf7567"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:43.431593Z","signature_b64":"mMlQvf0hC6UQocJvQpqc5i5Kki+9y8S3flubRw4vL3UL8Fgv1wHyhJrAjfCnVGb4UIw8HkwMhzW6hxTSawMUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9622eb4495c1f907a1747a7442f3cf7c5dcc104793246304925dc8a104888d8","last_reissued_at":"2026-05-18T00:58:43.430962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:43.430962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unirationality of Hurwitz spaces of coverings of degree <= 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vassil Kanev","submitted_at":"2011-06-06T10:21:19Z","abstract_excerpt":"Let $Y$ be a smooth, projective curve of genus $g\\geq 1$ over the complex numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings $p:X \\to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy group equal to $S_d$, and $det(p_{*}O_X/O_Y)$ isomorphic to a fixed line bundle $A^{-1}$ of degree $-e$. We prove that, when $d=3, 4$ or $5$ and $n$ is sufficiently large (precise bounds are given), these Hurwitz spaces are unirational. If in addition $(e,2)=1$ (when $d=3$), $(e,6)=1$ (when $d=4$) and $(e,10)=1$ (when $d=5$), then these Hurwitz spaces are rational."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1006","kind":"arxiv","version":6},"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":"1106.1006","created_at":"2026-05-18T00:58:43.431038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1006v6","created_at":"2026-05-18T00:58:43.431038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1006","created_at":"2026-05-18T00:58:43.431038+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FRC5NCJLQPZ","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FRC5NCJLQPZA6QX","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FRC5NCJ","created_at":"2026-05-18T12:26:22.705136+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/7FRC5NCJLQPZA6QXI6TUILZ467","json":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467.json","graph_json":"https://pith.science/api/pith-number/7FRC5NCJLQPZA6QXI6TUILZ467/graph.json","events_json":"https://pith.science/api/pith-number/7FRC5NCJLQPZA6QXI6TUILZ467/events.json","paper":"https://pith.science/paper/7FRC5NCJ"},"agent_actions":{"view_html":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467","download_json":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467.json","view_paper":"https://pith.science/paper/7FRC5NCJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1006&json=true","fetch_graph":"https://pith.science/api/pith-number/7FRC5NCJLQPZA6QXI6TUILZ467/graph.json","fetch_events":"https://pith.science/api/pith-number/7FRC5NCJLQPZA6QXI6TUILZ467/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467/action/storage_attestation","attest_author":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467/action/author_attestation","sign_citation":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467/action/citation_signature","submit_replication":"https://pith.science/pith/7FRC5NCJLQPZA6QXI6TUILZ467/action/replication_record"}},"created_at":"2026-05-18T00:58:43.431038+00:00","updated_at":"2026-05-18T00:58:43.431038+00:00"}