Modern Projective Geometry

  • Claude-Alain Faure
  • Alfred Frölicher

Part of the Mathematics and Its Applications book series (MAIA, volume 521)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Claude-Alain Faure, Alfred Frölicher
    Pages 1-24
  3. Claude-Alain Faure, Alfred Frölicher
    Pages 25-53
  4. Claude-Alain Faure, Alfred Frölicher
    Pages 55-79
  5. Claude-Alain Faure, Alfred Frölicher
    Pages 81-106
  6. Claude-Alain Faure, Alfred Frölicher
    Pages 107-125
  7. Claude-Alain Faure, Alfred Frölicher
    Pages 127-155
  8. Claude-Alain Faure, Alfred Frölicher
    Pages 157-186
  9. Claude-Alain Faure, Alfred Frölicher
    Pages 187-213
  10. Claude-Alain Faure, Alfred Frölicher
    Pages 215-234
  11. Claude-Alain Faure, Alfred Frölicher
    Pages 235-253
  12. Claude-Alain Faure, Alfred Frölicher
    Pages 255-273
  13. Claude-Alain Faure, Alfred Frölicher
    Pages 275-299
  14. Claude-Alain Faure, Alfred Frölicher
    Pages 301-322
  15. Claude-Alain Faure, Alfred Frölicher
    Pages 323-344
  16. Back Matter
    Pages 345-363

About this book

Introduction

Projective geometry is a very classical part of mathematics and one might think that the subject is completely explored and that there is nothing new to be added. But it seems that there exists no book on projective geometry which provides a systematic treatment of morphisms. We intend to fill this gap. It is in this sense that the present monograph can be called modern. The reason why morphisms have not been studied much earlier is probably the fact that they are in general partial maps between the point sets G and G, noted ' 9 : G -- ~ G', i.e. maps 9 : D -4 G' whose domain Dom 9 := D is a subset of G. We give two simple examples of partial maps which ought to be morphisms. The first example is purely geometric. Let E, F be complementary subspaces of a projective geometry G. If x E G \ E, then g(x) := (E V x) n F (where E V x is the subspace generated by E U {x}) is a unique point of F, i.e. one obtains a map 9 : G \ E -4 F. As special case, if E = {z} is a singleton and F a hyperplane with z tf. F, then g: G \ {z} -4 F is the projection with center z of G onto F.

Keywords

Lattice Volume matroid projective geometry quantum mechanics

Authors and affiliations

  • Claude-Alain Faure
    • 1
  • Alfred Frölicher
    • 1
  1. 1.University of GenevaGenevaSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9590-2
  • Copyright Information Springer Science+Business Media B.V. 2000
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5544-6
  • Online ISBN 978-94-015-9590-2
  • About this book
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