✦ LIBER ✦
A Result on Spreads of the Generalized QuadrangleT2(O), withOan Oval Arising from a Flock, and Applications
✍ Scribed by J.A. Thas
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 114 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
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✦ Synopsis
If F is a flock of the quadratic cone K of PG(3, q), q even, then the corresponding generalized quadrangle S(F) of order (q 2 , q) has subquadrangles T 2 (O), with O an oval, of order q. We prove in a geometrical way that any such T 2 (O) has spreads S consisting of an element y ∈ O and the q 2 lines not in the plane PG(2, q) of O of q quadratic cones K x , x ∈ O -{y}, of the space PG(3, q) containing T 2 (O), where K x has vertex x, is tangent to PG(2, q) at x y and has nucleus line xn, with n the nucleus of O. We also show how the oval O can be directly constructed from the flock F.