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 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.
Orbits of the Class O6 of Lines External to the Twisted Cubic in PG (3 , q)
Marcugini S.;Pambianco F.
2023
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 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.File in questo prodotto:
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