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

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Description

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.
Release date NZ
December 15th, 2010
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 2000
Illustrations
XVII, 363 p.
Pages
363
Dimensions
155x235x20
ISBN-13
9789048155446
Product ID
8963672

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