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Topics in Finite Geometry
Ovals, Ovoids and
Generalized Quadrangles
S. E. Payne

Table of Contents 

1 Synthetic Axioms for Geometry

2 Analytic Geometry

3 The Fundamental Theorem for P G(n, q)

4 The Ubiquitous Oval

5 Quadratic Forms

6 Quadrics in P G(3, q)

7 Ovoids in 3-Dimensional Space

8 Trace Equations

9 Finite Generalized Quadrangles

10 GQ Associated with an Oval or Ovoid

11 Classifiying Ovoids - Part 2

12 The Klein Correspondence

13 q-Clans and Their Geometries

14 Finite Circle Geometries

15 Property G

16 Laguerre Geometries and GQ

17 Translation Oval Cones

18 Generalized Fans and Spreads of T2 (O))

19 Appendix 1: Some Elementary Number Theory

20 Appendix 2: Algebra in Fq [x]

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