Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

Conics in Baer subplanes

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

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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).

Article information

Source
Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 2 (2019), 85-107.

Dates
Received: 4 July 2018
Revised: 4 December 2018
Accepted: 29 December 2018
First available in Project Euclid: 5 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1559700153

Digital Object Identifier
doi:10.2140/iig.2019.17.85

Mathematical Reviews number (MathSciNet)
MR3956900

Zentralblatt MATH identifier
07062414

Subjects
Primary: 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

Keywords
Bruck–Bose representation Baer subplanes conics subconics

Citation

Barwick, Susan G.; Jackson, Wen-Ai; Wild, Peter. Conics in Baer subplanes. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 2, 85--107. doi:10.2140/iig.2019.17.85. https://projecteuclid.org/euclid.iig/1559700153


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