{"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"}