{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:NF5YVSAMERX3I6EWSSLG7RFSES","short_pith_number":"pith:NF5YVSAM","schema_version":"1.0","canonical_sha256":"697b8ac80c246fb4789694966fc4b224aba98e20377f9d57c359ebe87b31b5c1","source":{"kind":"arxiv","id":"math/0408130","version":1},"attestation_state":"computed","paper":{"title":"Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ch. Okonek, M. Duerr","submitted_at":"2004-08-10T11:42:23Z","abstract_excerpt":"In [DKO] we constructed virtual fundamental classes $[[ Hilb^m_V ]]$ for Hilbert schemes of divisors of topological type m on a surface V, and used these classes to define the Poincare invariant of V:\n  (P^+_V,P^-_V): H^2(V,Z) --> \\Lambda^* H^1(V,Z) x \\Lambda^* H^1(V,Z)\n We conjecture that this invariant coincides with the full Seiberg-Witten invariant computed with respect to the canonical orientation data.\n  In this note we prove that the existence of an integral curve $C \\subset V$ induces relations between some of these virtual fundamental classes $[[Hilb^m_V ]]$. The corresponding relatio"},"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":"math/0408130","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-08-10T11:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"6798503f3a7ef94b1add7ec5efd299c54c282830419a76f2d49dbab253c898d6","abstract_canon_sha256":"f86ab46104105a9cbdb06df4eb2715eacd9f8348457abc2357e4d7aaf96d3036"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:26.119746Z","signature_b64":"Mv1xnGRuNuQUF+e9R0we60IZYiBZTDsPkAYcpGdlR10LyQexUZtTDA2z58BYhcl3ea1yD7a01PldWSHw3SQHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"697b8ac80c246fb4789694966fc4b224aba98e20377f9d57c359ebe87b31b5c1","last_reissued_at":"2026-05-18T01:05:26.119092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:26.119092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ch. Okonek, M. Duerr","submitted_at":"2004-08-10T11:42:23Z","abstract_excerpt":"In [DKO] we constructed virtual fundamental classes $[[ Hilb^m_V ]]$ for Hilbert schemes of divisors of topological type m on a surface V, and used these classes to define the Poincare invariant of V:\n  (P^+_V,P^-_V): H^2(V,Z) --> \\Lambda^* H^1(V,Z) x \\Lambda^* H^1(V,Z)\n We conjecture that this invariant coincides with the full Seiberg-Witten invariant computed with respect to the canonical orientation data.\n  In this note we prove that the existence of an integral curve $C \\subset V$ induces relations between some of these virtual fundamental classes $[[Hilb^m_V ]]$. The corresponding relatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408130","kind":"arxiv","version":1},"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":"math/0408130","created_at":"2026-05-18T01:05:26.119192+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0408130v1","created_at":"2026-05-18T01:05:26.119192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408130","created_at":"2026-05-18T01:05:26.119192+00:00"},{"alias_kind":"pith_short_12","alias_value":"NF5YVSAMERX3","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"NF5YVSAMERX3I6EW","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"NF5YVSAM","created_at":"2026-05-18T12:25:52.687210+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/NF5YVSAMERX3I6EWSSLG7RFSES","json":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES.json","graph_json":"https://pith.science/api/pith-number/NF5YVSAMERX3I6EWSSLG7RFSES/graph.json","events_json":"https://pith.science/api/pith-number/NF5YVSAMERX3I6EWSSLG7RFSES/events.json","paper":"https://pith.science/paper/NF5YVSAM"},"agent_actions":{"view_html":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES","download_json":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES.json","view_paper":"https://pith.science/paper/NF5YVSAM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0408130&json=true","fetch_graph":"https://pith.science/api/pith-number/NF5YVSAMERX3I6EWSSLG7RFSES/graph.json","fetch_events":"https://pith.science/api/pith-number/NF5YVSAMERX3I6EWSSLG7RFSES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES/action/storage_attestation","attest_author":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES/action/author_attestation","sign_citation":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES/action/citation_signature","submit_replication":"https://pith.science/pith/NF5YVSAMERX3I6EWSSLG7RFSES/action/replication_record"}},"created_at":"2026-05-18T01:05:26.119192+00:00","updated_at":"2026-05-18T01:05:26.119192+00:00"}