Pub. Date:
Springer Netherlands
Modern Projective Geometry / Edition 1

Modern Projective Geometry / Edition 1

by Claude-Alain Faure, Alfred Frölicher
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This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.

Product Details

ISBN-13: 9789048155446
Publisher: Springer Netherlands
Publication date: 12/10/2010
Series: Mathematics and Its Applications , #521
Edition description: Softcover reprint of the original 1st ed. 2000
Pages: 363
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Preface. Introduction. 1. Fundamental Notions of Lattice Theory. 2. Projective Geometries and Projective Lattices. 3. Closure Spaces and Matroids. 4. Dimension Theory. 5. Geometries of degree n. 6. Morphisms of Projective Geometries. 7. Embeddings and Quotient-Maps. 8. Endomorphisms and the Desargues Property. 9. Homogeneous Coordinates. 10. Morphisms and Semilinear Maps. 11. Duality. 12. Related Categories. 13. Lattices of Closed Subspaces. 14. Orthogonality. List of Problems. Bibliography. List of Axioms. List of Symbols. Index.

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