Orbits of the class O₆ of lines external with respect to the twisted cubic in PG(3,q)

2022/09/11 by Davydov, Alexander A., Marcugini, Stefano, Pambianco, Fernanda
#51E21 51E22 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.04910

Abstract

In the projective space PG(3,q), we consider orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of PG(3,q) are partitioned into classes, each of which is a union of line orbits. We propose an approach to obtain orbits of the class named O₆, whose complete classification is an open problem. For all even and odd q we describe a family of orbits of O₆ and their stabilizer groups. The orbits of this family include an essential part of all O₆ orbits.

Related

• Twisted cubic and orbits of lines in PG(3,q)
• Twisted cubic and orbits of lines in PG(3,q), II
• Further results on orbits and incidence matrices for the class O₆ of lines external to the twisted cubic in PG(3,q)
• Incidence matrices for the class O₆ of lines external to the twisted cubic in PG(3,q)
• Incidence of lines, points, and planes in PG(3,q) with respect to the twisted cubic