{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:I67WVGIQXCJGDVTLOELPNZPFQ2","short_pith_number":"pith:I67WVGIQ","schema_version":"1.0","canonical_sha256":"47bf6a9910b89261d66b7116f6e5e586954240cbb3c4b107bb35059a6c1b5fbf","source":{"kind":"arxiv","id":"1304.5709","version":3},"attestation_state":"computed","paper":{"title":"Logarithmic Bundles Of Hypersurface Arrangements In P^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini","submitted_at":"2013-04-21T08:59:13Z","abstract_excerpt":"Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \\Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that \\Omega^{1}_{P^n}(log D) admits a resolution of lenght 1 which explicitly depends on the degrees and on the equations of D_{1},...,D_{l}. Then we prove a Torelli type theorem when all the D_{i}'s have the same degree d and l >= {{n+d} \\choose {d}}+3: indeed, we recover the components of D as unstable smooth hypersurfaces of \\Omega^{1}_{P^n}(log D). Finally we analyze the"},"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":"1304.5709","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-21T08:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"a5f044afbc2de344e4989e0e179fb561ee3eaa31d620415967e4ae33561ccf51","abstract_canon_sha256":"10fef0f16ac97274c7ee6286715e71ebddb8ec726acabd072e12dc4dc95502c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:00.117994Z","signature_b64":"BCmmJDGhwaXXNe9fFmikU5aZT6jxaDQYjsSooRxZl+SDkHR1Hb8wPUaZ0Ar/s9jO+QcKapZZSk7iAqLlXDoDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47bf6a9910b89261d66b7116f6e5e586954240cbb3c4b107bb35059a6c1b5fbf","last_reissued_at":"2026-05-18T01:56:00.117572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:00.117572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic Bundles Of Hypersurface Arrangements In P^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini","submitted_at":"2013-04-21T08:59:13Z","abstract_excerpt":"Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \\Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that \\Omega^{1}_{P^n}(log D) admits a resolution of lenght 1 which explicitly depends on the degrees and on the equations of D_{1},...,D_{l}. Then we prove a Torelli type theorem when all the D_{i}'s have the same degree d and l >= {{n+d} \\choose {d}}+3: indeed, we recover the components of D as unstable smooth hypersurfaces of \\Omega^{1}_{P^n}(log D). Finally we analyze the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5709","kind":"arxiv","version":3},"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":"1304.5709","created_at":"2026-05-18T01:56:00.117637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.5709v3","created_at":"2026-05-18T01:56:00.117637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5709","created_at":"2026-05-18T01:56:00.117637+00:00"},{"alias_kind":"pith_short_12","alias_value":"I67WVGIQXCJG","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I67WVGIQXCJGDVTL","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I67WVGIQ","created_at":"2026-05-18T12:27:46.883200+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/I67WVGIQXCJGDVTLOELPNZPFQ2","json":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2.json","graph_json":"https://pith.science/api/pith-number/I67WVGIQXCJGDVTLOELPNZPFQ2/graph.json","events_json":"https://pith.science/api/pith-number/I67WVGIQXCJGDVTLOELPNZPFQ2/events.json","paper":"https://pith.science/paper/I67WVGIQ"},"agent_actions":{"view_html":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2","download_json":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2.json","view_paper":"https://pith.science/paper/I67WVGIQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.5709&json=true","fetch_graph":"https://pith.science/api/pith-number/I67WVGIQXCJGDVTLOELPNZPFQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/I67WVGIQXCJGDVTLOELPNZPFQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2/action/storage_attestation","attest_author":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2/action/author_attestation","sign_citation":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2/action/citation_signature","submit_replication":"https://pith.science/pith/I67WVGIQXCJGDVTLOELPNZPFQ2/action/replication_record"}},"created_at":"2026-05-18T01:56:00.117637+00:00","updated_at":"2026-05-18T01:56:00.117637+00:00"}