{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UA7ZSXF7BEF3PAZ3NLDDAV2BCR","short_pith_number":"pith:UA7ZSXF7","schema_version":"1.0","canonical_sha256":"a03f995cbf090bb7833b6ac63057411458f4644a37ea9645a794fd40674e7ee5","source":{"kind":"arxiv","id":"1907.06705","version":1},"attestation_state":"computed","paper":{"title":"On the Iitaka Conjecture $C_{n,m}$ for K\\\"ahler Fibre Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Juanyong Wang","submitted_at":"2019-07-15T19:17:37Z","abstract_excerpt":"By applying the positivity theorem of direct images and a pluricanonical version of the structure theorem on the cohomology jumping loci \\`a la Green-Lazarsfeld-Simpson, we show that the klt K\\\"ahler version of the Iitaka conjecture $C_{n,m}$ (Ueno, 1975) for $f:X\\to Y$ (surjective morphism between compact K\\\"ahler manifolds with connected general fibre) holds true when the determinant of the direct image of some power of the relative canonical bundle is big on $Y$ or when $Y$ is a complex torus. These generalize the corresponding results of Viehweg (1983) and of Cao-P\\u aun (2017) respectivel"},"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":"1907.06705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-15T19:17:37Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"d84eb32b62424d3e1cc787aa3c018558f971f2f02c613569dd1a9469612ff35e","abstract_canon_sha256":"ba4119c18f6590272cb03418fde41ffb9634f43c7489085eefc9ff12a2cb2239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:29.393072Z","signature_b64":"Dwi6BSxJO9/UaazZM5hmeX0CvBi99jb4u+g/GQETz3JaN903yexal3FyVlHaHcEp1o+nXsYCgZqkhLDMy7nuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a03f995cbf090bb7833b6ac63057411458f4644a37ea9645a794fd40674e7ee5","last_reissued_at":"2026-05-17T23:40:29.392535Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:29.392535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Iitaka Conjecture $C_{n,m}$ for K\\\"ahler Fibre Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Juanyong Wang","submitted_at":"2019-07-15T19:17:37Z","abstract_excerpt":"By applying the positivity theorem of direct images and a pluricanonical version of the structure theorem on the cohomology jumping loci \\`a la Green-Lazarsfeld-Simpson, we show that the klt K\\\"ahler version of the Iitaka conjecture $C_{n,m}$ (Ueno, 1975) for $f:X\\to Y$ (surjective morphism between compact K\\\"ahler manifolds with connected general fibre) holds true when the determinant of the direct image of some power of the relative canonical bundle is big on $Y$ or when $Y$ is a complex torus. These generalize the corresponding results of Viehweg (1983) and of Cao-P\\u aun (2017) respectivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06705","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":"1907.06705","created_at":"2026-05-17T23:40:29.392593+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.06705v1","created_at":"2026-05-17T23:40:29.392593+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06705","created_at":"2026-05-17T23:40:29.392593+00:00"},{"alias_kind":"pith_short_12","alias_value":"UA7ZSXF7BEF3","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UA7ZSXF7BEF3PAZ3","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UA7ZSXF7","created_at":"2026-05-18T12:33:30.264802+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/UA7ZSXF7BEF3PAZ3NLDDAV2BCR","json":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR.json","graph_json":"https://pith.science/api/pith-number/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/graph.json","events_json":"https://pith.science/api/pith-number/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/events.json","paper":"https://pith.science/paper/UA7ZSXF7"},"agent_actions":{"view_html":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR","download_json":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR.json","view_paper":"https://pith.science/paper/UA7ZSXF7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.06705&json=true","fetch_graph":"https://pith.science/api/pith-number/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/graph.json","fetch_events":"https://pith.science/api/pith-number/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/action/storage_attestation","attest_author":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/action/author_attestation","sign_citation":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/action/citation_signature","submit_replication":"https://pith.science/pith/UA7ZSXF7BEF3PAZ3NLDDAV2BCR/action/replication_record"}},"created_at":"2026-05-17T23:40:29.392593+00:00","updated_at":"2026-05-17T23:40:29.392593+00:00"}