Parlato, Laura (2009) Ovoids and spreads of Q+(7,q). [Tesi di dottorato] (Unpublished)

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Abstract

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 [14] and J.A. Thas in [22]. 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 [7] and Dye [8].

Item Type: Tesi di dottorato
Uncontrolled Keywords: Unitary ovoid, unitary spread, slice
Depositing User: Francesca Migliorini
Date Deposited: 03 Dec 2009 10:02
Last Modified: 30 Apr 2014 19:40
URI: http://www.fedoa.unina.it/id/eprint/4221

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