{"paper":{"title":"Exterior splashes and linear sets of rank 3","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":"2014-04-07T01:32:01Z","abstract_excerpt":"In $\\PG(2,q^3)$, let $\\pi$ be a subplane of order $q$ that is exterior to $\\li$. The exterior splash of $\\pi$ is defined to be the set of $q^2+q+1$ points on $\\li$ that lie on a line of $\\pi$. This article investigates properties of an exterior \\orsp\\ and its exterior splash. We show that the following objects are projectively equivalent: exterior splashes, covers of the circle geometry $CG(3,q)$, Sherk surfaces of size $q^2+q+1$, and $\\GF(q)$-linear sets of rank 3 and size $q^2+q+1$. We compare our construction of exterior splashes with the projection construction of a linear set. We give a g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1641","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"}