On elliptic ovoids and their rosettes in a classical generalized quadrangle of even order
Abstract
Let Q_0 be the classical generalized quadrangle of order q = 2n arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry X having as points all the elliptic ovoids of Q_0 and as lines the maximal pencils of elliptic ovoids of Q_0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q \setminus Q_0 where Q is the classical (q; q^2)-generalized quadrangle admitting Q_0 as a hyperplane. Then, we investigate the collinearity graph \Gamma of X: In particular, we obtain a classification of the cliques of \Gamma proving that they arise either from lines of Q or subgeometries of Q defined over F_2
Keywords
Cite
@article{arxiv.1403.1714,
title = {On elliptic ovoids and their rosettes in a classical generalized quadrangle of even order},
author = {Ilaria Cardinali and N. S. Narasimha Sastry},
journal= {arXiv preprint arXiv:1403.1714},
year = {2014}
}