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We first prove that $Y$ is a klt Fano variety if ${\\rm deg} \\, f \\ge C$ for some constant $C = C(n, d)$ depending only on $n$ and $d$. Next we prove an optimal upper bound ${\\rm deg} \\, f \\le {\\rm deg} \\, X$ provided that $Y$ is factorial, ${\\rm deg} \\, f$ is prime and ${\\rm deg} \\, f \\ge E(n)$ for some constant $E(n)$ (with $E(n) = n(n+1)$ when $Y$ is smooth). As a corollary, we show that $Y\\cong {\\bf P}^"},"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":"1908.06894","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-19T15:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"374eec8b10653ea8f9b90808aac78f32a915f41824bf03b2c84ad3e33ddca199","abstract_canon_sha256":"26227bc3005f46a0a30aee09ec8890f7ac90ec6a22733326120506188a669255"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:05.788878Z","signature_b64":"3R1LXoFNYCUNjki6z5e0YEle6PD9pz1L6PXiQyDaPOEoIsusmsuz7Ez6fmhZN/WFDmS5u10VHZooPH6wIREqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7d2d9aa698ff2162e0c704756d7b9fba5c5eb47ff31756329dcd52386568a3d","last_reissued_at":"2026-06-11T01:09:05.785892Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:05.785892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morphisms from a very general hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"De-Qi Zhang, Yongnam Lee, Yujie Luo","submitted_at":"2019-08-19T15:52:53Z","abstract_excerpt":"Let $X$ be a very general hypersurface of degree $d$ in the projective $(n+1)$-space with $n \\ge 3$, and $f: X \\to Y$ a non-birational surjective morphism to a normal projective variety $Y$. We first prove that $Y$ is a klt Fano variety if ${\\rm deg} \\, f \\ge C$ for some constant $C = C(n, d)$ depending only on $n$ and $d$. Next we prove an optimal upper bound ${\\rm deg} \\, f \\le {\\rm deg} \\, X$ provided that $Y$ is factorial, ${\\rm deg} \\, f$ is prime and ${\\rm deg} \\, f \\ge E(n)$ for some constant $E(n)$ (with $E(n) = n(n+1)$ when $Y$ is smooth). As a corollary, we show that $Y\\cong {\\bf P}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06894","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06894/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.06894","created_at":"2026-06-11T01:09:05.786203+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06894v6","created_at":"2026-06-11T01:09:05.786203+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06894","created_at":"2026-06-11T01:09:05.786203+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7JNTKTJR7ZB","created_at":"2026-06-11T01:09:05.786203+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7JNTKTJR7ZBMLQM","created_at":"2026-06-11T01:09:05.786203+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7JNTKTJ","created_at":"2026-06-11T01:09:05.786203+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/U7JNTKTJR7ZBMLQMOBDVNV5Z7O","json":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O.json","graph_json":"https://pith.science/api/pith-number/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/graph.json","events_json":"https://pith.science/api/pith-number/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/events.json","paper":"https://pith.science/paper/U7JNTKTJ"},"agent_actions":{"view_html":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O","download_json":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O.json","view_paper":"https://pith.science/paper/U7JNTKTJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06894&json=true","fetch_graph":"https://pith.science/api/pith-number/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/graph.json","fetch_events":"https://pith.science/api/pith-number/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/action/storage_attestation","attest_author":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/action/author_attestation","sign_citation":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/action/citation_signature","submit_replication":"https://pith.science/pith/U7JNTKTJR7ZBMLQMOBDVNV5Z7O/action/replication_record"}},"created_at":"2026-06-11T01:09:05.786203+00:00","updated_at":"2026-06-11T01:09:05.786203+00:00"}