Orbits of the stabiliser group of the Segre variety product of three projective lines

2012/07/17 by Michel Lavrauw, Lavrauw, Michel, John Sheekey +1
Mathematics · #Algebraic Geometry and Number Theory #math.CO

paper · pdf · doi:10.48550/arxiv.1207.3972

arxiv created 2012/07/17 · arxiv updated 2012/07/18

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.

Related

• Canonical forms of 2× 3 × 3 tensors over the real field, algebraically closed fields, and finite fields
• The symmetric representation of lines in PG(\mathbbF³ ⊗ \mathbbF³)
• Equations for the third secant variety of the Segre product of n projective spaces
• Twisted cubic and orbits of lines in PG(3,q)
• Orbits of the class O₆ of lines external with respect to the twisted cubic in PG(3,q)