Modern projective geometry

by Claude-Alain Faure and Alfred Frölicher

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.

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  • 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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書名 Modern projective geometry
著作者等 Frölicher, Alfred
Frolicher Alfred
Faure Claude-Alain
シリーズ名 Mathematics and its applications
出版元 Kluwer Academic
刊行年月 c2000
ページ数 xvii, 363 p.
大きさ 25 cm
ISBN 0792365259
NCID BA49014386
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言語 英語
出版国 オランダ