2013/08/21 by S. G. Barwick, Wen-Ai Jackson, Barwick, S. G. +2
Mathematics · #51E20 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO #msc:51E20
paper · pdf · doi:10.48550/arxiv.1308.4484
arxiv created 2013/08/21 · openalex publication_date 2013/08/21 · arxiv updated 2013/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a non-degenerate conic in \PG(2,q2), q odd, that is tangent to ℓ_∞ 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,q2). That is, we define a set \C in \PG(4,q) with q2 points that satisfies certain combinatorial properties. We then show that if q≥ 7, we can use \C to construct a regular spread § in the hyperplane at infinity of \PG(4,q), and that \C corresponds to a conic in the Desarguesian plane ¶(§)≅\PG(2,q2) constructed via the Bruck-Bose correspondence.