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 [Tesi di dottorato] (Unpublished)


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Item Type: Tesi di dottorato
Language: English
Title: Ovoids and spreads of Q+(7,q)
Date: 30 November 2009
Number of Pages: 58
Institution: Università degli Studi di Napoli Federico II
Department: Matematica e applicazioni "Renato Caccioppoli"
Doctoral School: Scienze matematiche e informatiche
PHD name: Scienze matematiche
PHD cycle: 22
PHD Coordinator:
De Giovanni, FrancescoUNSPECIFIED
Date: 30 November 2009
Number of Pages: 58
Uncontrolled Keywords: Unitary ovoid, unitary spread, slice
MIUR S.S.D.: Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria
Date Deposited: 03 Dec 2009 10:02
Last Modified: 30 Apr 2014 19:40
DOI: 10.6092/UNINA/FEDOA/4221


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].

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