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.

Contains many applications to coding theory, algebraic geometry, incidence geometry, design theory, graph theory, and group theory Provides detailed studies of quadrics, Hermitian varieties, Grassmann varieties, Veronese and Segre varieties Unique being the only book of its kind

Autorentext

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.

Inhalt

Preface.- Terminology.- Quadrics.- Hermitian varieties.- Grassmann varieties.- Veronese and Serge varieties.- Embedded geometries.- Arcs and Caps.- Ovoids, spreads and m-systems of finite polar spaces.- References.- Index.