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BL
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| Record Number
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666265
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dltt
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| Main Entry
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Hirschfeld, J. W. P., (James William Peter),1940-
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| Title & Author
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General Galois geometries /\ J.W.P. Hirschfeld, J.A. Thas
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| Series Statement
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Springer monographs in mathematics,
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| Page. NO
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1 online resource (xvii, 409 pages) :: color illustrations.
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| ISBN
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9781447167907
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: 1447167902
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9781447167884
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| Bibliographies/Indexes
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Includes bibliographical references and idnex
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| Contents
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Preface; Status of the subject; Related topics; Acknowledgements; Terminology; PART V; 1 Quadrics; 1.1 Canonical forms; 1.2 Invariants; 1.3 Tangency and polarity; 1.4 Generators; 1.5 Numbers of subspaces on a quadric; 1.6 The orthogonal groups; 1.7 The polarity reconsidered; 1.8 Sections of non-singular quadrics; 1.9 Parabolic sections of parabolic quadrics; 1.10 The characterisation of quadrics; 1.11 Further characterisations of quadrics; 1.12 The Principle of Triality; 1.13 Generalised hexagons; 1.14 Notes and references; Sections 1.1-1.9; Section 1.10; Section 1.11
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Sections 1.12-1.132 Hermitian varieties; 2.1 Introduction; 2.2 Tangency and polarity; 2.3 Generators and sub-generators; 2.4 Sections of Un; 2.5 The characterisation of Hermitian varieties; 2.6 The characterisation of projections of quadrics; 2.7 Notes and references; Sections 2.1-2.3; Section 2.4; Sections 2.5-2.6; 3 Grassmann varieties; 3.1 Plücker and Grassmann coordinates; 3.2 Grassmann varieties; 3.3 A characterisation of Grassmann varieties; 3.4 Embedding of Grassmann spaces; 3.5 Notes and references; Section 3.1; Section 3.2; Section 3.3; Section 3.4; 4 Veronese and Segre varieties
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4.1 Veronese varieties4.2 Characterisations; 4.2.1 Characterisations of V2n n of the first kind; 4.2.2 Characterisations of V2n n of the second kind; 4.2.3 Characterisations of V2n n of the third kind; 4.2.4 Characterisations of V2n n of the fourth kind; 4.3 Hermitian Veroneseans; 4.4 Characterisations of Hermitian Veroneseans; 4.4.1 Characterisations of Hn,n2+2n of the first kind; 4.4.2 Characterisations of Hn,n2+2n of the third kind; 4.4.3 Characterisations of H2,8 of the fourth kind; 4.5 Segre varieties; 4.6 Regular n-spreads and Segre varieties S1; n
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4.6.1 Construction method for n-spreads of PG (2n + 1,q)4.7 Notes and references; Section 4.1; Section 4.2; Section 4.3; Section 4.4; Section 4.5; Section 4.6; 5 Embedded geometries; 5.1 Polar spaces; 5.2 Generalised quadrangles; 5.3 Embedded Shult spaces; 5.4 Lax and polarised embeddings of Shult spaces; 5.5 Characterisations of the classical generalised quadrangles; 5.6 Partial geometries; 5.7 Embedded partial geometries; 5.8 (0, Ü)-geometries and semi-partial geometries; 5.9 Embedded (0, Ü)-geometries and semi-partial geometries; 5.10 Notes and references; Section 5.1; Section 5.2
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Section 5.3Section 5.4; Section 5.5; Section 5.6; Section 5.7; Section 5.8; Section 5.9; 6 Arcs and caps; 6.1 Introduction; 6.2 Caps and codes; 6.3 The maximum size of a cap for q odd; 6.4 The maximum size of a cap for q even; 6.5 General properties of k-arcs and normal rational curves; 6.6 The maximum size of an arc and the characterisation of such arcs; 6.7 Arcs and hypersurfaces; 6.8 Notes and References; Section 6.1; Section 6.2; Section 6.3; Section 6.4; Section 6.5; Section 6.6; Section 6.7; 7 Ovoids, spreads and m-systems of finite classical polar spaces
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| Abstract
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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
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| Subject
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Geometry, Projective.
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| Subject
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Galois theory.
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| Dewey Classification
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516/.5
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| LC Classification
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QA471
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| Added Entry
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Thas, J. A., (Joseph Adolf)
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Ohio Library and Information Network.
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