This thesis concerns sets of points in the finite projective space PG(n,q) that are combinatorially identical to quadrics. A quadric is the set of points of PG(n,q) whose coordinates satisfy a quadradic equation, and the term quadral is used in this thesis to mean a set of points with all the combinatorial properties of a quadric. Most of the thesis concerns the characterisation of certain sets of subspaces associated with quadrals. Characterisations are proved for the external lines of an oval cone in PG(3,q), of a non-singular quadric in PG(4,q), q even, and of a large class of cones in PG(n,q), q even. Characterisations are also proved for the planes meeting the non-singular quadric of PG(4,q) in a non-singular conic, and for the tangents and generator lines of this quadric for q odd. The second part of the thesis is concerned with the intersection of ovoids of PG(3,q). A new bound is proved on the number of points two ovoids can share, and configurations of secants and external lines that two ovoids can share are determined. The structure of ovoidal fibrations is discussed, and this is used to prove new results on the intersection of two ovoids sharing all of their tangents. / Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2008
| Identifer | oai:union.ndltd.org:ADTP/264542 |
| Date | January 2008 |
| Creators | Butler, David Keith |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
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