Parlato, Laura
(2009)
Ovoids and spreads of Q+(7,q).
[Tesi di dottorato]
(Unpublished)
| Item Type: |
Tesi di dottorato
|
| Lingua: |
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 |
| Uncontrolled Keywords: |
Unitary ovoid, unitary spread, slice |
| Settori scientifico-disciplinari del MIUR: |
Area 01 - Scienze matematiche e informatiche > MAT/03 - Geometria |
[error in script]
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| 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 |
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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