Orbits of the Class O6 of Lines External to the Twisted Cubic in PG(3,q)

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 O 6 , whose c...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2023-06, Vol.20 (3)
Main Authors: Davydov, Alexander A., Marcugini, Stefano, Pambianco, Fernanda
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Orbital stability
Orbits
Online Access:Get full text
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Summary: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 O 6 , whose complete classification is an open problem. For all q , we describe a family of orbits of O 6 and their stabilizer groups. The orbits of this family include an essential part of all O 6 orbits.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02349-7