General Galois Geometries

Projective spaces over a finite field, otherwise known as Galois geometries, find wide application in coding theory, algebraic geometry, design theory, graph theory, and group theory as well as being beautiful objects of study in their own right. This volume is the culmination of a three volume treatise on this subject. With its companion volumes "Projective Geometries Over Finite Fields" and "Finite Projective Spaces of Three Dimensions" this work should provide a major reference to the subject. It is essentially self-contained and will be an invaluable companion for research workers and postgraduate students working on these topics. The authors study three main themes: the study of algebraic varieties over finite fields, the combinatorics of Galois geometries, and the identification of various incidence structures associated with them. In particular much attention is devoted to Hermitian varieties, to Grassmannian varieties, and to polar spaces.Table of ContentTerminology; Quadrics; Hermitian varieties; Grassmann varieties; Veronese and Segre varieties; Embedded geometries; Arcs and caps; Appendix VI. Ovoids and spreads of finite classical polar spaces; Appendix VII. Errata for Finite projective spaces of three dimensions and Projective geometries over finite fields; Bibliography; Index of notation; Author index; General index.