Modern Projective Geometry by Claude-Alain FaureModern Projective Geometry by Claude-Alain Faure

Modern Projective Geometry

byClaude-Alain Faure, Alfred Frölicher

Paperback | December 15, 2010

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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.
Title:Modern Projective GeometryFormat:PaperbackDimensions:363 pagesPublished:December 15, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048155444

ISBN - 13:9789048155446


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.