Claude-Alain Faure

(Author)

Modern Projective Geometry (2000)Hardcover - 2000, 30 September 2000

Modern Projective Geometry (2000)
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Part of Series
Mathematics and Its Applications
Print Length
363 pages
Language
English
Publisher
Springer
Date Published
30 Sep 2000
ISBN-10
0792365259
ISBN-13
9780792365259

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.

Product Details

Authors:
Claude-Alain FaureAlfred Frölicher
Book Edition:
2000
Book Format:
Hardcover
Country of Origin:
US
Date Published:
30 September 2000
Dimensions:
23.39 x 15.6 x 2.24 cm
ISBN-10:
0792365259
ISBN-13:
9780792365259
Language:
English
Location:
Dordrecht
Pages:
363
Publisher:
Weight:
716.68 gm

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