Specialness and the Bose representation

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

paper

Specialness and the Bose representation

arXiv:1906.03295

Abstract

This article looks at subconics of order $q$ of $P G (2, q^{2})$ and characterizes them in the Bruck-Bose representation in $P G (4, q)$ . In common with other objects in the Bruck-Bose representation, the characterisation uses the transversals of the regular line spread $S$ associated with the Bruck-Bose representation.By working in the Bose representation of $P G (2, q^{2})$ in $P G (5, q)$ , we give a geometric explanation as to why the transversals of the regular spread $S$ are intrinsic to the characterisation of varieties of $P G (2, q^{2})$ .