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Quaderni Elettronici del Seminario di Geometria Combinatoria
2E (Maggio 2001), 1--54 Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica |
Chapter 1 is a brief introduction to projective spaces and
concludes with the basic idea of how to see PG(n-1,q) and
AG(n,q) as subsets of elements of the field GF(qn).
Chapter 2
introduces some interesting subsets of points found in projective
spaces, in particular maximal arcs in finite projective planes and
introduces related incidence structures such as inversive planes
and partial geometries. We also prove a theorem about maximal arcs
using finite fields.
Chapter 3 is an introduction to polar spaces including
representing the classical polar spaces as subsets of finite
fields. The section is concluded with the introduction of
m-systems of polar spaces and the construction of maximal arcs
from particular m-systems.
Chapter 4 contains a very brief introduction to generalised
quadrangles and is mainly concerned with ovoids and spreads of the
symplectic generalised quadrangle which are again considered as
subsets of finite fields.