{"paper":{"title":"On the Hilbert scheme of linearly normal curves in $\\mathbb{P}^r$ of relatively high degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Changho Keem, Claudio Fontanari, Edoardo Ballico","submitted_at":"2019-04-15T16:41:27Z","abstract_excerpt":"Let $\\mathcal{H}_{d,g,r}$ be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree $d$ and genus $g$ in $\\PP^r$. We denote by $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ the union of those components of $\\mathcal{H}_{d,g,r}$ whose general element is linearly normal and we show that any non-empty $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ ($d\\ge g+r-3$) is irreducible for an extensive range of triples $(d,g,r)$ beyond the Brill-Noether range. This establishes the validity of a suitably modified assertion of Severi regarding the irreducibility of the Hilbert scheme $\\mathcal{H}^\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07716","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"}