On ovoids, generalized quadrangles, spreads and inversive planes
This thesis shows the relationship of ovoids in PG(3, q), q 2, to finite generalized quadrangles, spreads in PG(3, q) and finite inversive planes. An ovoid in PG(3, q) is determined from an ovoid in the W(q) generalized quadrangle. Specifically, the set of absolute points of a polarity in W(q) for q...
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| Format: | text |
| Language: | English |
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Animo Repository
1994
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/1641 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This thesis shows the relationship of ovoids in PG(3, q), q 2, to finite generalized quadrangles, spreads in PG(3, q) and finite inversive planes. An ovoid in PG(3, q) is determined from an ovoid in the W(q) generalized quadrangle. Specifically, the set of absolute points of a polarity in W(q) for q = 2 2e+1, e greater than or equal to 1, determines the Tits ovoid. Also, a generalized quadrangle of order (q, q2) is constructed from an ovoid. For q = 2h, h 1, it is shown that the determination of ovoids is equivalent to the determination of spreads belonging to a general linear complex in PG(3, q).From an ovoid, an inversive plane of order q 2 is constructed. Conversely, a method of constructing an ovoid from an inversive plane of order q 2 is presented. It is proved that such a construction can surely be done if q is even, that is, that every inversive plane of even order is egglike. It is also shown that an inversive plane is egglike if and only if it admits an orthogonality. Hence, an ovoid can be constructed from an inversive plane of odd order if it admits an orthogonality. |
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