Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Abstract

Let Q0 be the classical generalized quadrangle of order q = 2n (n ≥ 2) 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 Q0 and as lines the maximal pencils of elliptic ovoids of Q0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q \ Q0, where Q is the classical (q, q2)- generalized quadrangle admitting Q0 as a hyperplane. Further, we classify the cliques in the collinearity graph is either a line of X or it consists of 6 or 4 points of X not contained in any line of X, accordingly as n is odd or even.We count the number of cliques of each type and show that those cliques which are not contained in lines of X arise as subgeometries of Q defined over F2.

First Page

591

Last Page

612

DOI

10.1007/s12044-016-0311-6

Publication Date

11-1-2016

Link to Full Text

Share

COinS