{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6MJ2HYMB5XKDI5QDOGS3LYD7JH","short_pith_number":"pith:6MJ2HYMB","schema_version":"1.0","canonical_sha256":"f313a3e181edd434760371a5b5e07f49eb612e2e7c9a3f8909f3b7b1d0103f1c","source":{"kind":"arxiv","id":"1410.8047","version":2},"attestation_state":"computed","paper":{"title":"Theta-regularity of curves and Brill-Noether loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luigi Lombardi, Wenbo Niu","submitted_at":"2014-10-29T16:29:42Z","abstract_excerpt":"We provide a bound on the $\\Theta$-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an \"abelian\" version of Gruson-Lazarsfeld-Peskine's bound on the Castelnuovo--Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus of a curve in a (non necessarily principally) polarized abelian variety. Finally, we bound the $\\Theta$-regularity of a class of higher dimensional subvarieties in Jacobian varieties, i.e. the Bri"},"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":"1410.8047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-29T16:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"87b0422ce7217a9ab4131eba05ceb97c9ee09d8a002a5afe6c964f1f157c1423","abstract_canon_sha256":"0b91f2b8a176107229bc8640917621ae6a592be26e6673d803ea052dcb34bedf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:26.891650Z","signature_b64":"mYNcBWpCJRcK8G2dqZj6I6Kd60VzA3duR/Gsf1tboP6jks3boo4ooIYytEDbLq+QORsPbNvNYMox24nSTnxeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f313a3e181edd434760371a5b5e07f49eb612e2e7c9a3f8909f3b7b1d0103f1c","last_reissued_at":"2026-05-18T02:07:26.891137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:26.891137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theta-regularity of curves and Brill-Noether loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luigi Lombardi, Wenbo Niu","submitted_at":"2014-10-29T16:29:42Z","abstract_excerpt":"We provide a bound on the $\\Theta$-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an \"abelian\" version of Gruson-Lazarsfeld-Peskine's bound on the Castelnuovo--Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus of a curve in a (non necessarily principally) polarized abelian variety. Finally, we bound the $\\Theta$-regularity of a class of higher dimensional subvarieties in Jacobian varieties, i.e. the Bri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8047","kind":"arxiv","version":2},"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":"1410.8047","created_at":"2026-05-18T02:07:26.891206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8047v2","created_at":"2026-05-18T02:07:26.891206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8047","created_at":"2026-05-18T02:07:26.891206+00:00"},{"alias_kind":"pith_short_12","alias_value":"6MJ2HYMB5XKD","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6MJ2HYMB5XKDI5QD","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6MJ2HYMB","created_at":"2026-05-18T12:28:16.859392+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/6MJ2HYMB5XKDI5QDOGS3LYD7JH","json":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH.json","graph_json":"https://pith.science/api/pith-number/6MJ2HYMB5XKDI5QDOGS3LYD7JH/graph.json","events_json":"https://pith.science/api/pith-number/6MJ2HYMB5XKDI5QDOGS3LYD7JH/events.json","paper":"https://pith.science/paper/6MJ2HYMB"},"agent_actions":{"view_html":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH","download_json":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH.json","view_paper":"https://pith.science/paper/6MJ2HYMB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8047&json=true","fetch_graph":"https://pith.science/api/pith-number/6MJ2HYMB5XKDI5QDOGS3LYD7JH/graph.json","fetch_events":"https://pith.science/api/pith-number/6MJ2HYMB5XKDI5QDOGS3LYD7JH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH/action/storage_attestation","attest_author":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH/action/author_attestation","sign_citation":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH/action/citation_signature","submit_replication":"https://pith.science/pith/6MJ2HYMB5XKDI5QDOGS3LYD7JH/action/replication_record"}},"created_at":"2026-05-18T02:07:26.891206+00:00","updated_at":"2026-05-18T02:07:26.891206+00:00"}