{"paper":{"title":"On the coincidence of Pascal lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jaydeep Chipalkatti","submitted_at":"2014-07-06T00:30:08Z","abstract_excerpt":"Let ${\\mathcal K}$ denote a smooth conic in the complex projective plane. Pascal's theorem says that, given six points $A,B,C,D,E,F$ on ${\\mathcal K}$, the three intersection points $AE \\cap BF, AD \\cap CF, BD \\cap CE$ are collinear. This defines the Pascal line of the array $\\left[ \\begin{array}{ccc} A & B & C \\\\ F & E & D \\end{array} \\right]$, and one gets sixty such lines in general by permuting the points. In this paper we consider the variety $\\Psi$ of sextuples $\\{A, \\dots, F\\}$, for which some of these Pascal lines coincide. We show that $\\Psi$ has two irreducible components: a five-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1447","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"}