{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DDKSRNUOLFGMZAA4K6K5MFDPPV","short_pith_number":"pith:DDKSRNUO","schema_version":"1.0","canonical_sha256":"18d528b68e594ccc801c5795d6146f7d4289473974344067c8dc215da36df2d5","source":{"kind":"arxiv","id":"1502.06258","version":5},"attestation_state":"computed","paper":{"title":"On the canonical divisor of smooth toroidal compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AG","authors_text":"Gabriele Di Cerbo, Luca F. Di Cerbo","submitted_at":"2015-02-22T18:40:12Z","abstract_excerpt":"In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three. Moreover, if $n\\geq 3$ we show that the numerical dimension of the canonical divisor of a smooth $n$-dimensional compactification is always bigger or equal to $n-1$. We also show that up to a finite \\'etale cover all such compactifications have ample canonical class, therefore refining a classical theorem of Mumford and Tai. Finally, we improve in all dimensions $n\\geq 3$ the cusp count for finite volume complex hype"},"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":"1502.06258","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-22T18:40:12Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"080bfe176bc0473af2bc2935ef75d3a5c7ca6b6705bd4099748c9a1fa94bc9e3","abstract_canon_sha256":"ab6c87549aed340a0a896534c8c7207febf65e0bde6ae7a43a63d391a618f30c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:55.764540Z","signature_b64":"tvHg7RPMvEdtrHSkSPJLzufhZCuMAAYiHW5YDpXUPtLW8SPg1p7kD/1kVtkUeSEibZR1k3p3yRSdGe0anxOVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18d528b68e594ccc801c5795d6146f7d4289473974344067c8dc215da36df2d5","last_reissued_at":"2026-05-18T00:32:55.763832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:55.763832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the canonical divisor of smooth toroidal compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.AG","authors_text":"Gabriele Di Cerbo, Luca F. Di Cerbo","submitted_at":"2015-02-22T18:40:12Z","abstract_excerpt":"In this paper, we show that the canonical divisor of a smooth toroidal compactification of a complex hyperbolic manifold must be nef if the dimension is greater or equal to three. Moreover, if $n\\geq 3$ we show that the numerical dimension of the canonical divisor of a smooth $n$-dimensional compactification is always bigger or equal to $n-1$. We also show that up to a finite \\'etale cover all such compactifications have ample canonical class, therefore refining a classical theorem of Mumford and Tai. Finally, we improve in all dimensions $n\\geq 3$ the cusp count for finite volume complex hype"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06258","kind":"arxiv","version":5},"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":"1502.06258","created_at":"2026-05-18T00:32:55.763940+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06258v5","created_at":"2026-05-18T00:32:55.763940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06258","created_at":"2026-05-18T00:32:55.763940+00:00"},{"alias_kind":"pith_short_12","alias_value":"DDKSRNUOLFGM","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DDKSRNUOLFGMZAA4","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DDKSRNUO","created_at":"2026-05-18T12:29:17.054201+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/DDKSRNUOLFGMZAA4K6K5MFDPPV","json":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV.json","graph_json":"https://pith.science/api/pith-number/DDKSRNUOLFGMZAA4K6K5MFDPPV/graph.json","events_json":"https://pith.science/api/pith-number/DDKSRNUOLFGMZAA4K6K5MFDPPV/events.json","paper":"https://pith.science/paper/DDKSRNUO"},"agent_actions":{"view_html":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV","download_json":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV.json","view_paper":"https://pith.science/paper/DDKSRNUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06258&json=true","fetch_graph":"https://pith.science/api/pith-number/DDKSRNUOLFGMZAA4K6K5MFDPPV/graph.json","fetch_events":"https://pith.science/api/pith-number/DDKSRNUOLFGMZAA4K6K5MFDPPV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV/action/storage_attestation","attest_author":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV/action/author_attestation","sign_citation":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV/action/citation_signature","submit_replication":"https://pith.science/pith/DDKSRNUOLFGMZAA4K6K5MFDPPV/action/replication_record"}},"created_at":"2026-05-18T00:32:55.763940+00:00","updated_at":"2026-05-18T00:32:55.763940+00:00"}