Parlato, Laura (2009) Ovoids and spreads of Q+(7,q). [Tesi di dottorato] (Unpublished)
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| Item Type: | Tesi di dottorato |
|---|---|
| Resource language: | English |
| Title: | Ovoids and spreads of Q+(7,q) |
| Creators: | Creators Email Parlato, Laura laura.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" |
| Scuola di dottorato: | Scienze matematiche e informatiche |
| Dottorato: | Scienze matematiche |
| Ciclo di dottorato: | 22 |
| Coordinatore del Corso di dottorato: | nome email De Giovanni, Francesco UNSPECIFIED |
| Tutor: | nome email Lunardon, Guglielmo lunardon@unina.it |
| Date: | 30 November 2009 |
| Number of Pages: | 58 |
| Keywords: | Unitary ovoid, unitary spread, slice |
| Settori scientifico-disciplinari del MIUR: | 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 |
| DOI: | 10.6092/UNINA/FEDOA/4221 |
Collection description
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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