A Classification of the Veldkamp Lines of the Near Hexagon L_3 times GQ(2, 2)

Richard M. Green (1) , Metod Saniga (2)

1 Department of Mathematics, University of Colorado
2 Astronomical Institute of the Slovak Academy of Sciences

Using a standard technique sometimes (inaccurately) known as Burnside's Lemma, it is shown that the Veldkamp space of the near hexagon L_3 times GQ(2, 2) features 156 different types of lines. We also give an explicit description of each type of a line by listing the types of the three geometric hyperplanes it consists of and describing the properties of its core set, that is the subset of points of L_3 times GQ(2, 2) shared by the three geometric hyperplanes in question.

Mots clés: Near Hexagons; Geometric Hyperplanes; Veldkamp Spaces

Domaines: Combinatoire [math.CO]; Physique mathématique [math-ph]; Géométrie algébrique [math.AG]; Physique mathématique [math-ph]

Richard M. Green, Metod Saniga. A Classification of the Veldkamp Lines of the Near Hexagon L_3 times GQ(2, 2). 2015. ⟨hal-00871875v2⟩