{"paper":{"title":"Characterising pointsets in PG(4,q) that correspond to conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S.G. Barwick, Wen-Ai Jackson","submitted_at":"2013-08-21T05:01:23Z","abstract_excerpt":"We consider a non-degenerate conic in $\\PG(2,q^2)$, $q$ odd, that is tangent to $\\ell_\\infty$ and look at its structure in the Bruck-Bose representation in $\\PG(4,q)$. We determine which combinatorial properties of this set of points in $\\PG(4,q)$ are needed to reconstruct the conic in $\\PG(2,q^2)$. That is, we define a set $\\C$ in $\\PG(4,q)$ with $q^2$ points that satisfies certain combinatorial properties. We then show that if $q\\ge 7$, we can use $\\C$ to construct a regular spread $\\S$ in the hyperplane at infinity of $\\PG(4,q)$, and that $\\C$ corresponds to a conic in the Desarguesian plan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4484","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"}