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.
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This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume).
This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces.
General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Both authors have been active in the field for about a half century. They have authored several books and several hundreds of papers in international journals; they have also been keynote speakers at numerous international conferences, as well as having organised such conferences. The standard works on Galois geometries and finite generalised quadrangles are due to them as authors or co-authors.
James Hirschfeld was born and brought up in Sydney, and studied at Sydney and Edinburgh. He has been at Sussex since 1966.
Joseph Thas studied at Ghent University, where he has held positions since 1966. He has been a member of the Royal Flemish Academy of Belgium for Science and the Arts since 1988.
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