{"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. We give exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06149","kind":"arxiv","version":2},"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"}