Twisted cubic and orbits of lines in $\mathrm{PG}(3,q)$
Combinatorics
2021-03-29 v2
Abstract
In the projective space , we consider the orbits of lines under the stabilizer group of the twisted cubic. It is well known that the lines can be partitioned into classes every of which is a union of line orbits. All types of lines forming a unique orbit are found. For the rest of the line types (apart from one of them) it is proved that they form exactly two or three orbits; sizes and structures of these orbits are determined. Problems remaining open for one type of lines are formulated. For and , they are solved.
Cite
@article{arxiv.2103.12655,
title = {Twisted cubic and orbits of lines in $\mathrm{PG}(3,q)$},
author = {Alexander A. Davydov and Stefano Marcugini and Fernanda Pambianco},
journal= {arXiv preprint arXiv:2103.12655},
year = {2021}
}
Comments
27 pages, 19 references. arXiv admin note: text overlap with arXiv:2103.11248. Some misprints are corrected, pages 1-2 edited