{"paper":{"title":"Irreducibility and components rigid in moduli of the Hilbert scheme of smooth curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Angelo Felice Lopez, Changho Keem, Yun-Hwan Kim","submitted_at":"2016-05-01T19:47:50Z","abstract_excerpt":"Denote by $\\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, that is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\\mathbb P^r$. A component of $\\mathcal{H}_{d,g,r}$ is rigid in moduli if its image under the natural map $\\pi:\\mathcal{H}_{d,g,r} \\dashrightarrow \\mathcal{M}_{g}$ is a one point set. In this note, we provide a proof of the fact that $\\mathcal{H}_{d,g,r}$ has no components rigid in moduli for $g > 0$ and $r=3$, from which it follows that the only smooth projective curves embedded in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00297","kind":"arxiv","version":3},"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"}