Twisted cubic and orbits of lines in $\mathrm{PG}(3,q)$, II
Combinatorics
2022-01-03 v1
Abstract
In the projective space , we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of are partitioned into classes, each of which is a union of line orbits. In this paper, all classes of lines consisting of a unique orbit are found. For the remaining line types, with one exception, it is proved that they consist exactly of two or three orbits; sizes and structures of these orbits are determined. Also, the subgroups of the stabilizer group of the twisted cubic fixing lines of the orbits are obtained. Problems which remain open for one type of lines are formulated and, for and , a solution is provided.
Cite
@article{arxiv.2112.14803,
title = {Twisted cubic and orbits of lines in $\mathrm{PG}(3,q)$, II},
author = {Alexander A. Davydov and Stefano Marcugini and Fernanda Pambianco},
journal= {arXiv preprint arXiv:2112.14803},
year = {2022}
}
Comments
6 pages, 21 references. arXiv admin note: text overlap with arXiv:2103.11248