# Modern Projective Geometry

• Claude-Alain Faure
• Alfred Frölicher
Book

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

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

### 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