Orbits of the stabiliser group of the Segre variety product of three projective lines
Michel Lavrauw, John Sheekey
TL;DR
This paper analyzes the action of the stabiliser group of a Segre variety of three projective lines, revealing the orbit structure on singular and all points over different fields.
Contribution
It characterizes the orbit structure of the stabiliser group acting on points of the Segre variety, including the number of orbits over finite and infinite fields.
Findings
Four orbits on singular points over any field
Five orbits on all points over finite fields
Detailed orbit classification for the stabiliser group
Abstract
We prove that the stabiliser group G of the Segre variety product in PG(V) of three projective lines over a field F has four orbits on singular points of PG(V), and that G has five orbits on points of PG(V) if F is finite.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Coding theory and cryptography