{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:VQXERMSS7IQFH66AH53EIAVJRI","short_pith_number":"pith:VQXERMSS","schema_version":"1.0","canonical_sha256":"ac2e48b252fa2053fbc03f764402a98a0407a173806f19d3cb5bae1fad17a264","source":{"kind":"arxiv","id":"math/0411253","version":1},"attestation_state":"computed","paper":{"title":"On Symplectic Coverings of the Projective Plane","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"G.-M. Greuel, Vik.S. Kulikov","submitted_at":"2004-11-11T10:21:24Z","abstract_excerpt":"We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\\bar H$ and, maybe, along a line \"at infinity\" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\\\"{a}hler symplectic form (assuming that if $\\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\\bar{H}$ are investigated and applied to the calculation of the first B"},"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/0411253","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2004-11-11T10:21:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"fb1aa5e911b5ee09774b207eaf5f679341f2ded7f34af22f43cdf98cb2cd099c","abstract_canon_sha256":"e08927639a0b3d189b8431accc2e3895b766dc538b20261ec91a83eddf910f5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:27.033684Z","signature_b64":"KiEwL/Rcpanv+1lyWRBoQIjiI+2Jp7U1SDHZEcYa0pmBukRYjBuD3shYH9ncTqTbZPTuXUL7rV3e4unv26ekAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac2e48b252fa2053fbc03f764402a98a0407a173806f19d3cb5bae1fad17a264","last_reissued_at":"2026-05-18T01:38:27.033029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:27.033029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Symplectic Coverings of the Projective Plane","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"G.-M. Greuel, Vik.S. Kulikov","submitted_at":"2004-11-11T10:21:24Z","abstract_excerpt":"We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\\bar H$ and, maybe, along a line \"at infinity\" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\\\"{a}hler symplectic form (assuming that if $\\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\\bar{H}$ are investigated and applied to the calculation of the first B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411253","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/0411253","created_at":"2026-05-18T01:38:27.033114+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411253v1","created_at":"2026-05-18T01:38:27.033114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411253","created_at":"2026-05-18T01:38:27.033114+00:00"},{"alias_kind":"pith_short_12","alias_value":"VQXERMSS7IQF","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"VQXERMSS7IQFH66A","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"VQXERMSS","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/VQXERMSS7IQFH66AH53EIAVJRI","json":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI.json","graph_json":"https://pith.science/api/pith-number/VQXERMSS7IQFH66AH53EIAVJRI/graph.json","events_json":"https://pith.science/api/pith-number/VQXERMSS7IQFH66AH53EIAVJRI/events.json","paper":"https://pith.science/paper/VQXERMSS"},"agent_actions":{"view_html":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI","download_json":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI.json","view_paper":"https://pith.science/paper/VQXERMSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411253&json=true","fetch_graph":"https://pith.science/api/pith-number/VQXERMSS7IQFH66AH53EIAVJRI/graph.json","fetch_events":"https://pith.science/api/pith-number/VQXERMSS7IQFH66AH53EIAVJRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI/action/storage_attestation","attest_author":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI/action/author_attestation","sign_citation":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI/action/citation_signature","submit_replication":"https://pith.science/pith/VQXERMSS7IQFH66AH53EIAVJRI/action/replication_record"}},"created_at":"2026-05-18T01:38:27.033114+00:00","updated_at":"2026-05-18T01:38:27.033114+00:00"}