# Modern Projective Geometry

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

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

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.

Lattice Volume matroid projective geometry quantum mechanics

- 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
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