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 [Tesi di dottorato] (Unpublished)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)
Creators:
CreatorsEmail
Parlato, Lauralaura.parlato@gmail.com
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:
nameemail
De Giovanni, FrancescoUNSPECIFIED
Tutor:
nameemail
Lunardon, Guglielmolunardon@unina.it
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
URI: http://www.fedoa.unina.it/id/eprint/4221

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].

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