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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 $(Hilb P^3)_{red}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0505413","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-05-19T11:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"e62ab21eee4028f81fa912b66a615ed8d852c3280d3ec7831ceb00c5a3fc0996","abstract_canon_sha256":"c228d9738889ab3ed0fae99d6d6ef26b9d9469be858d706912d717acbda69535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.636262Z","signature_b64":"3AvvC+YyMT4RNV28+ciHQN+7G458u6nV/asS2g/O6nzjY1X0G4k07kHmYBJSElnRg/Dw403iXxdqbFmBn42ZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c40a2c789034e3adb8ba5390866920fbae6bf962746a97ff4a404e7e1b3b761","last_reissued_at":"2026-05-18T01:21:45.635755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.635755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $P^3$. 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