{"paper":{"title":"On the Hilbert scheme of curves in higher-dimensional projective space","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Barbara Fantechi, Rita Pardini","submitted_at":"1995-01-17T15:27:37Z","abstract_excerpt":"In this paper we prove that, for any $n\\ge 3$, there exist infinitely many $r\\in \\N$ and for each of them a smooth, connected curve $C_r$ in $\\P^r$ such that $C_r$ lies on  exactly $n$ irreducible components of the Hilbert scheme $\\hilb(\\P^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9501009","kind":"arxiv","version":1},"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"}