Vol. 17, No. 2, 2019

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Conics in Baer subplanes

Susan G. Barwick, Wen-Ai Jackson and Peter Wild

Vol. 17 (2019), No. 2, 85–107
Abstract

This article studies conics and subconics of PG(2,q2) and their representation in the André/Bruck–Bose setting in PG(4,q). In particular, we investigate their relationship with the transversal lines of the regular spread. The main result is to show that a conic in a tangent Baer subplane of PG(2,q2) corresponds in PG(4,q) to a normal rational curve that meets the transversal lines of the regular spread. Conversely, every 3- and 4-dimensional normal rational curve in PG(4,q) that meets the transversal lines of the regular spread corresponds to a conic in a tangent Baer subplane of PG(2,q2).

Keywords
Bruck–Bose representation, Baer subplanes, conics, subconics
Mathematical Subject Classification 2010
Primary: 51E20
Milestones
Received: 4 July 2018
Revised: 4 December 2018
Accepted: 29 December 2018
Published: 14 March 2019
Authors
Susan G. Barwick
School of Mathematical Sciences
University of Adelaide
Australia
Wen-Ai Jackson
School of Mathematical Sciences
University of Adelaide
Australia
Peter Wild
University of London
United Kingdom