{"paper":{"title":"Obstructions to deforming space curves and non-reduced components of the Hilbert scheme","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hirokazu Nasu","submitted_at":"2005-05-19T11:02:06Z","abstract_excerpt":"Let $Hilb P^3$ denote the Hilbert scheme of smooth connected curves in $P^3$. We consider maximal irreducible closed subsets $W \\subset Hilb P^3$ whose general member $C$ is contained in a smooth cubic surface and investigate the conditions for $W$ to be a component of $(Hilb P^3)_{red}$. We especially study the case where the dimension of the tangent space of $Hilb P^3$ at $[C]$ is greater than $\\dim W$ by one. We compute obstructions to deforming $C$ in $P^3$ and prove that for every $W$ in this case, $Hilb P^3$ is non-reduced along $W$ and $W$ is a component of $(Hilb P^3)_{red}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505413","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"}