Incidence matrices for the class $${\mathcal {O}}_6$$ of lines external to the twisted cubic in $$\textrm{PG}(3,q)$$

Davydov, Alexander A.; Marcugini, Stefano; Pambianco, Fernanda

doi:10.1007/s00022-023-00678-2

Cited by 1 publication

(3 citation statements)

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“…In [16], using the properties of the orbits O µ and O L from [15], we determine all the plane-line and point-line incidence matrices connected with these orbits.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the Plücker embedding for the Klein quadric is applied. So, in [22], the methods and approaches are different with our published articles [12][13][14][15][16] and with this paper. Also, in [22], unlike this paper, the incidence matrices are not considered and the stabilizer groups on language of PG(3, q) are not presented.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we continue and develop approaches of [15,16]. We propose a new family of lines L ρ , where ρ is a parameter running over F * q .…”

Section: Introductionmentioning

confidence: 99%

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Orbits of Lines for a Twisted Cubic in $$\textrm{PG}(3,q)$$

2023

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In the literature, lines of the projective space PG(3, q) are partitioned into classes, each of which is a union of line orbits under the stabilizer group of the twisted cubic. The least studied class is named O 6 . This class contains lines external to the twisted cubic which are not its chords or axes and do not lie in any of its osculating planes. For even and odd q, we propose a new family of orbits of O 6 and investigate in detail their stabilizer groups and the corresponding submatrices of the point-line and plane-line incidence matrices. To obtain these submatrices, we explored the number of solutions of cubic and quartic equations connected with intersections of lines (including the tangents to the twisted cubic), points, and planes in PG(3, q).

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“…In [16], using the properties of the orbits O µ and O L from [15], we determine all the plane-line and point-line incidence matrices connected with these orbits.…”

Section: Introductionmentioning

confidence: 99%