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000753671 1001_ $$aHirschfeld, J. W. P.$$q(James William Peter),$$d1940-$$eauthor.
000753671 24510 $$aGeneral Galois geometries$$h[electronic resource] /$$cJ.W.P. Hirschfeld, J.A. Thas.
000753671 264_1 $$aLondon :$$bSpringer,$$c2016.
000753671 300__ $$a1 online resource (xvii, 409 pages) :$$bcolor illustrations.
000753671 336__ $$atext$$btxt$$2rdacontent
000753671 337__ $$acomputer$$bc$$2rdamedia
000753671 338__ $$aonline resource$$bcr$$2rdacarrier
000753671 4901_ $$aSpringer monographs in mathematics,$$x1439-7382
000753671 504__ $$aIncludes bibliographical references and idnex.
000753671 5050_ $$aPreface; Status of the subject; Related topics; Acknowledgements; Terminology; PART V; 1 Quadrics; 1.1 Canonical forms; 1.2 Invariants; 1.3 Tangency and polarity; 1.4 Generators; 1.5 Numbers of subspaces on a quadric; 1.6 The orthogonal groups; 1.7 The polarity reconsidered; 1.8 Sections of non-singular quadrics; 1.9 Parabolic sections of parabolic quadrics; 1.10 The characterisation of quadrics; 1.11 Further characterisations of quadrics; 1.12 The Principle of Triality; 1.13 Generalised hexagons; 1.14 Notes and references; Sections 1.1-1.9; Section 1.10; Section 1.11
000753671 5058_ $$aSections 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
000753671 5058_ $$a4.1 Veronese varieties4.2 Characterisations; 4.2.1 Characterisations of V2n n of the first kind; 4.2.2 Characterisations of V2n n of the second kind; 4.2.3 Characterisations of V2n n of the third kind; 4.2.4 Characterisations of V2n n of the fourth kind; 4.3 Hermitian Veroneseans; 4.4 Characterisations of Hermitian Veroneseans; 4.4.1 Characterisations of Hn,n2+2n of the first kind; 4.4.2 Characterisations of Hn,n2+2n of the third kind; 4.4.3 Characterisations of H2,8 of the fourth kind; 4.5 Segre varieties; 4.6 Regular n-spreads and Segre varieties S1; n
000753671 5058_ $$a4.6.1 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, α)-geometries and semi-partial geometries; 5.9 Embedded (0, α)-geometries and semi-partial geometries; 5.10 Notes and references; Section 5.1; Section 5.2
000753671 5058_ $$aSection 5.3Section 5.4; Section 5.5; Section 5.6; Section 5.7; Section 5.8; Section 5.9; 6 Arcs and caps; 6.1 Introduction; 6.2 Caps and codes; 6.3 The maximum size of a cap for q odd; 6.4 The maximum size of a cap for q even; 6.5 General properties of k-arcs and normal rational curves; 6.6 The maximum size of an arc and the characterisation of such arcs; 6.7 Arcs and hypersurfaces; 6.8 Notes and References; Section 6.1; Section 6.2; Section 6.3; Section 6.4; Section 6.5; Section 6.6; Section 6.7; 7 Ovoids, spreads and m-systems of finite classical polar spaces
000753671 506__ $$aAccess limited to authorized users.
000753671 520__ $$aThis book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
000753671 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed February 16, 2016).
000753671 650_0 $$aGeometry, Projective.
000753671 650_0 $$aGalois theory.
000753671 7001_ $$aThas, J. A.$$q(Joseph Adolf),$$eauthor.
000753671 77608 $$iPrint version:$$aHirschfeld, J.W.P$$tGeneral Galois Geometries$$dLondon : Springer London,c2016$$z9781447167884
000753671 830_0 $$aSpringer monographs in mathematics.
000753671 852__ $$bebk
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