{"paper":{"title":"Normal bundles of lines on hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hannah Larson","submitted_at":"2017-05-04T18:42:12Z","abstract_excerpt":"Let $X \\subset \\mathbb{P}^n$ be a smooth hypersurface. Given a sequence of integers $\\vec{a} = (a_1, \\ldots, a_{n-2})$ with $a_1 \\leq \\cdots \\leq a_{n-2}$, let $F_{\\vec{a}}(X)$ be the parameter space of lines $L$ on $X$ such that $N_{L/X} \\cong \\mathcal{O}(a_1) \\oplus \\cdots \\oplus \\mathcal{O}(a_{n-2})$. The loci $F_{\\vec{a}}(X)$ form a stratification of the Fano scheme of lines on $X$. We show that for general hypersurfaces, the $F_{\\vec{a}}(X)$ have the expected dimension and, in this case, compute the class of $\\overline{F_{\\vec{a}}(X)}$ in the Chow ring of the Grassmannian of lines in $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01972","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"}