{"paper":{"title":"Secants, bitangents, and their congruences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bernt Ivar Utst{\\o}l N{\\o}dland, Kathl\\'en Kohn, Paolo Tripoli","submitted_at":"2017-01-13T16:25:17Z","abstract_excerpt":"A congruence is a surface in the Grassmannian $\\mathrm{Gr}(1,\\mathbb{P}^3)$ of lines in projective $3$-space. To a space curve $C$, we associate the Chow hypersurface in $\\mathrm{Gr}(1,\\mathbb{P}^3)$ consisting of all lines which intersect $C$. We compute the singular locus of this hypersurface, which contains the congruence of all secants to $C$. A surface $S$ in $\\mathbb{P}^3$ defines the Hurwitz hypersurface in $\\mathrm{Gr}(1,\\mathbb{P}^3)$ of all lines which are tangent to $S$. We show that its singular locus has two components for general enough $S$: the congruence of bitangents and the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03711","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"}