{"paper":{"title":"On the geometry of the ricochet locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaydeep Chipalkatti","submitted_at":"2016-04-27T22:53:25Z","abstract_excerpt":"This paper is a study of the so-called `ricochet configuration' (or $R$-configuration) which arises in the context of Pascal's theorem. We give a geometric proof of the fact that a specific pair of Pascal lines is coincident for a sextuple in $R$-configuration. We calculate the symmetry group of a generic $R$-configuration, as well as the degree of the subvariety ${\\mathcal R} \\subseteq {\\mathbb P}^6$ of all such configurations. We also determine the $SL(2)$-equivariant defining equations for ${\\mathcal R}$, and show that it is an ideal-theoretic complete intersection of two invariant hypersur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08262","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"}