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Let $M(b_{\\bullet})$ be the space parameterizing nondegenerate, rational curves of degree $e$ in $\\mathbb{P}^n$ with ordinary singularities such that the normal bundle has the splitting type $\\bigoplus_{i=1}^{n-1}\\mathcal{O}(e+b_i)$. When $n=3$, celebrated results of Eisenbud, Van de Ven, Ghione and Sacchiero show that $M(b_{\\bullet})$ is irreducible of the expected dimension. We show that when $n \\geq 5$, these loci are generally reducible with components of higher than the expected dimension. We give exa"},"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":"1607.06149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-20T22:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"10a006e65192b6c0f93ffd159a44df472d94e6c7057451801e39adba3d89bc85","abstract_canon_sha256":"cf66a6371a87474308727eb27fa50df365d353361cc984893ae11cf02196a141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:23.850941Z","signature_b64":"DxG5+Pz7saIcxVomDQgqhBwfRVC04BCwAf1J79ORNCehaRigjI+81ccCxXk04Hz+M0dbm1q4nZgqcpC2372bCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3894baaa1b221854424995a3556bea7385f7393ea5364f4d4e5c4c9794625507","last_reissued_at":"2026-05-18T00:39:23.850281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:23.850281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal bundles of rational curves in projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eric Riedl, Izzet Coskun","submitted_at":"2016-07-20T22:59:28Z","abstract_excerpt":"Let $b_{\\bullet}$ be a sequence of integers $1 < b_1 \\leq b_2 \\leq \\cdots \\leq b_{n-1}$. Let $M(b_{\\bullet})$ be the space parameterizing nondegenerate, rational curves of degree $e$ in $\\mathbb{P}^n$ with ordinary singularities such that the normal bundle has the splitting type $\\bigoplus_{i=1}^{n-1}\\mathcal{O}(e+b_i)$. When $n=3$, celebrated results of Eisenbud, Van de Ven, Ghione and Sacchiero show that $M(b_{\\bullet})$ is irreducible of the expected dimension. We show that when $n \\geq 5$, these loci are generally reducible with components of higher than the expected dimension. 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