General Galois Geometries (Oxford Mathematical Monographs)

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9780198535379: General Galois Geometries (Oxford Mathematical Monographs)

"Generally speaking, every topic introduced in these volumes is treated with comprehensive thoroughness, mainly by using a concrete computational approach, and results are recorded with meticulous care. All this makes it possible for the reader to access results and follow arguments in any section with a minimal amount of back referencing to earlier sections, chapters or volumes. Taken together, these volumes constitute a monumental work of scholarship and are likely to be the standard reference in Galois geometry for the forseeable future."--Mathematical Reviews

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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.

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J.W.P. Hirschfeld , J.A. Thas
Editorial: Clarendon Press, Book
ISBN 10: 0198535376 ISBN 13: 9780198535379
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