Ovoids and spreads of Q+(7,q)
Parlato, Laura (2009) Ovoids and spreads of Q+(7,q). [Tesi di dottorato] (Inedito)
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This thesis concerns with slices of the unitary spread and of the unitary ovoid. The unitary spread and the unitary ovoid are geometric objects contained in the hyperbolic quadric Q+(7,q), if q equiv 2 (mod 3) and in the parabolic quadric Q(6; q), if q equiv 0 (mod 3); these were introduced by W.M. Kantor in  and J.A. Thas in . A slice of a spread (of an ovoid) of an orthogonal polar space is the intersection of the spread (of the ovoid) with a hyperplane of the relevant projective space. In this work, it is proved that the slices of the unitary spread of Q+(7,q) q equiv 2 (mod 3) can be divided into five classes. Slices belonging to different classes are inequivalent with respect to the action of the subgroup of PGammaO+(8; q)fixing the unitary spread. When q is even, there is a connection between spreads of Q+(7,q) and symplectic spreads of PG(5,q)originally pointed out by Dillon  and Dye .
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