{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YMWMK53XGDD4XNDKSG4Z7RCFTO","short_pith_number":"pith:YMWMK53X","schema_version":"1.0","canonical_sha256":"c32cc5777730c7cbb46a91b99fc4459b9f4e7890e3bf408dcc5da98c3d08cd1f","source":{"kind":"arxiv","id":"1408.7020","version":1},"attestation_state":"computed","paper":{"title":"Higher codimensional foliations and Kupka singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Arturo Fern\\'andez-P\\'erez, Maur\\'icio Corr\\^ea Jr, Omegar Calvo-Andrade","submitted_at":"2014-08-29T13:52:08Z","abstract_excerpt":"We consider holomorphic foliations of dimension $k>1$ and codimension $\\geq 1$ in the projective space $\\mathbb{P}^n$, with a compact connected component of the Kupka set. We prove that, if the transversal type is linear with positive integers eigenvalues, then the foliation consist on the fibers of a rational fibration. As a corollary, if $\\mathcal{F}$ is a foliation such that $dim(\\mathcal{F})\\geq cod(\\mathcal{F})+2$ and has transversal type diagonal with different eigenvalues, then the Kupka component $K$ is a complete intersection and we get the same conclusion. The same conclusion holds i"},"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":"1408.7020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-29T13:52:08Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"69c8f9c958f0d4703a61e95bd1d30e38d81bbb17998e633d3a9075d3b4692343","abstract_canon_sha256":"4fa4d6ef793e5eae012e2590ad98306557b89a7a460465387fef092949046b39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:37.671561Z","signature_b64":"6rbGWnNytu89wCk7A1Og7EV4+cr2OVtko9kptXbxdtIuf8Cxa1BHjA3Xt1eR8z9iTsD/OoUMddxkVmjhT68LBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32cc5777730c7cbb46a91b99fc4459b9f4e7890e3bf408dcc5da98c3d08cd1f","last_reissued_at":"2026-05-18T00:03:37.671005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:37.671005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher codimensional foliations and Kupka singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Arturo Fern\\'andez-P\\'erez, Maur\\'icio Corr\\^ea Jr, Omegar Calvo-Andrade","submitted_at":"2014-08-29T13:52:08Z","abstract_excerpt":"We consider holomorphic foliations of dimension $k>1$ and codimension $\\geq 1$ in the projective space $\\mathbb{P}^n$, with a compact connected component of the Kupka set. We prove that, if the transversal type is linear with positive integers eigenvalues, then the foliation consist on the fibers of a rational fibration. As a corollary, if $\\mathcal{F}$ is a foliation such that $dim(\\mathcal{F})\\geq cod(\\mathcal{F})+2$ and has transversal type diagonal with different eigenvalues, then the Kupka component $K$ is a complete intersection and we get the same conclusion. The same conclusion holds i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.7020","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":"1408.7020","created_at":"2026-05-18T00:03:37.671090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.7020v1","created_at":"2026-05-18T00:03:37.671090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.7020","created_at":"2026-05-18T00:03:37.671090+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMWMK53XGDD4","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMWMK53XGDD4XNDK","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMWMK53X","created_at":"2026-05-18T12:28:57.508820+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/YMWMK53XGDD4XNDKSG4Z7RCFTO","json":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO.json","graph_json":"https://pith.science/api/pith-number/YMWMK53XGDD4XNDKSG4Z7RCFTO/graph.json","events_json":"https://pith.science/api/pith-number/YMWMK53XGDD4XNDKSG4Z7RCFTO/events.json","paper":"https://pith.science/paper/YMWMK53X"},"agent_actions":{"view_html":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO","download_json":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO.json","view_paper":"https://pith.science/paper/YMWMK53X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.7020&json=true","fetch_graph":"https://pith.science/api/pith-number/YMWMK53XGDD4XNDKSG4Z7RCFTO/graph.json","fetch_events":"https://pith.science/api/pith-number/YMWMK53XGDD4XNDKSG4Z7RCFTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO/action/storage_attestation","attest_author":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO/action/author_attestation","sign_citation":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO/action/citation_signature","submit_replication":"https://pith.science/pith/YMWMK53XGDD4XNDKSG4Z7RCFTO/action/replication_record"}},"created_at":"2026-05-18T00:03:37.671090+00:00","updated_at":"2026-05-18T00:03:37.671090+00:00"}