Finite Projective Spaces of Three Dimensions [Hardcover]

This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field. It is the second and core volume of a three-volume treatise on finite projective spaces, the first volume being Projective Geometrics Over Finite Fields (OUP, 1979). The present work restricts itself to three dimensions, and considers both topics which are analogous of geometry over the complex numbers and topics that arise out of the modern theory of incidence structures. The book also examines properties of four and five dimensions, fundamental applications to translation planes, simple groups, and coding theory.

15. Lines
16. Ovaloids and Quadrics
17. Spans, Spreads, and Packings
18.k-Caps
19. Hermitian Surfaces
20. Cubic Surfaces with 27 Lines
21. Twisted Cubics andk-Arcs
Appendix III. Order of and Isomorphisms among the Semi-Linear Groups
Appendix IV. The Numbe of Points on an Algebraic Variety
Appendix V. Errata forProjective geometries over finite fields(OUP, 1979)
Bibliography
Index of Notation
Author Index
General Index