Flocks of ovoids and hyperbolic quadrics in PG (3,Q)
Date of Publication
1993
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Algebraic Geometry | Educational Assessment, Evaluation, and Research | Educational Methods
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Dr. Arlene Pascasio
Defense Panel Chair
Dr. Severino Diesto,
Defense Panel Member
Dr. Aurora Trance
Dr. Blessilda Raposa
Abstract/Summary
This thesis gives a comprehensive account of the geometric structures and combinatorial properties of ovoids and hyperbolic quadrics in PG(3,q), a three-dimensional projective space of order q where q is a prime power. An ovoid of PG(3,q), q 2 is a set of q2 + 1 points such that no three of which are collinear. Moreover, a nondegenerate quadric in PG(3,q) is a set of points which satisfies a second degree homogeneous equation. There are three types of quadrics namely elliptic, hyperbolic and cone. The first two types are thoroughly discussed in this paper. Furthermore, this study deals with flocks of ovoids and hyperbolic quadrics. Finally, there are two types of flocks namely linear flock and nonlinear flock. This thesis gives an exposition of the theorems about flocks found in [5]. These main results are:1. Every flock of an ovoid in PG(3,q) with q even is linear.2. Any flock of an elliptic quadric in PG(3,q) with q odd is linear.3. Every flock of a hyperbolic quadric in PG(3,q) with q even is linear.4. In PG(3,q) where q is odd, every hyperbolic quadric has nonlinear flocks. This thesis gives a comprehensive account of the geometric structures and combinatorial properties of ovoids and hyperbolic quadrics in PG(3,q), a three-dimensional projective space of order q where q is a prime power. An ovoid of PG(3,q), q 2, is a set of q2 + 1 points such that no three of which are collinear. Moreover, a nondegenerate quadric in PG(3,q) is a set of points which satisfies a second degree homogeneous equation. There are three types of quadrics, namely, elliptic, hyperbolic and cone. The first two types are thoroughly discussed in this paper. Furthermore, this study deals with flocks of ovoids and hyperbolic quadrics. Finally, there are two types of flocks, namely, linear flock and non-linear flock. This thesis gives an exposition of the theorems about flocks. The main results are the following:1. Every flock of an ovoid in PG(3,q) with q even is linear.2. Any flock of an elliptic quadric in PG(3,q) wit
Abstract Format
html
Language
English
Format
Accession Number
TG02176
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
176 leaves
Keywords
Quadrics; Ovals; Mathematics -- Formulae; Geometry; Hyperbolic; xx1 Surfaces; xx3 Hyperbolic geometry
Recommended Citation
Go, J. T. (1993). Flocks of ovoids and hyperbolic quadrics in PG (3,Q). Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1510
