On ovoids, generalized quadrangles, spreads and inversive planes
Date of Publication
1994
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Arlene A. Pascasio
Defense Panel Chair
Severino Diesto
Defense Panel Member
Yolando Beronque
Severino Gervacio
Abstract/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.
Abstract Format
html
Language
English
Format
Accession Number
TG02361
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
252 leaves
Keywords
Geometry; Plane; Finite generalized quadrangles; Spaces; Generalized; Combinatorial geometry; Quadrangles; Generalized finite
Recommended Citation
Tan, C. (1994). On ovoids, generalized quadrangles, spreads and inversive planes. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1641
