A characterisation of Baer subplanes

2019/06/04 by Barwick, S. G., Jackson, Wen-Ai
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.04318

Abstract

Let K be a set of q²+2q+1 points in PG(4,q). We show that if every 3-space meets K in either one, two or three lines, a line and a non-degenerate conic, or a twisted cubic, then K is a ruled cubic surface. Moreover, K corresponds via the Bruck-Bose representation to a tangent Baer subplane of PG(2,q²). We use this to prove a characterisation in PG(2,q²) of a set of points B as a tangent Baer subplane by looking at the intersections of B with Baer-pencils.

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