Conics in Baer subplanes

S. G. Barwick; Wen-Ai Jackson; Peter Wild

paper

Conics in Baer subplanes

arXiv:1906.03296

Abstract

This article studies conics and subconics of $P G (2, q^{2})$ and their representation in the André/Bruck-Bose setting in $P G (4, q)$ . 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 $P G (2, q^{2})$ corresponds in $P G (4, q)$ to a normal rational curve that meets the transversal lines of the regular spread. Conversely, every 3 and 4-dimensional normal rational curve in $P G (4, q)$ that meets the transversal lines of the regular spread corresponds to a conic in a tangent Baer subplane of $P G (2, q^{2})$ .