{"paper":{"title":"Gonality of curves on general hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ciro Ciliberto, Flaminio Flamini, Francesco Bastianelli, Paola Supino","submitted_at":"2017-07-23T06:30:12Z","abstract_excerpt":"This paper concerns the existence of curves with low gonality on smooth hypersurfaces of sufficiently large degree. It has been recently proved that if $X\\subset \\mathbb{P}^{n+1}$ is a hypersurface of degree $d\\geq n+2$, and if $C\\subset X$ is an irreducible curve passing through a general point of $X$, then its gonality verifies $\\mathrm{gon}(C)\\geq d-n$, and equality is attained on some special hypersurfaces. We prove that if $X\\subset \\mathbb{P}^{n+1}$ is a very general hypersurface of degree $d\\geq 2n+2$, the least gonality of an irreducible curve $C\\subset X$ passing through a general poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07252","kind":"arxiv","version":2},"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"}