{"paper":{"title":"The exterior splash in $PG(6,q)$: Special 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":"2014-10-16T01:42:34Z","abstract_excerpt":"Let $\\pi$ be an order-$q$-subplane of $PG(2,q^3)$ that is exterior to $\\ell_\\infty$. The exterior splash of $\\pi$ is the set of $q^2+q+1$ points on $\\ell_\\infty$ that lie on an extended line of $\\pi$. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry $CG(3,q)$, and hyper-reguli of $PG(5,q)$. In this article we use the Bruck-Bose representation in $PG(6,q)$ to give a geometric characterisation of special conics of $\\pi$ in terms of the covers of the exterior splash of $\\pi$. We also investigate properties of order-$q$-subplanes\\ with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4269","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"}