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 will provide a major reference to the subject. It is essentially self-contained and will be an invaluable companion for research workers and post-graduate 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. The topics covered find application across a wide-range of topics in pure mathematics. The book will be useful to research workers and postgraduate students in combinatorics and geometry, and some computer scientists.