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.
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|Titolo:||Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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