Abstract
We start with the theorem that every non-degenerate morphism g: P V - - → P W is of the form g = P f for some semilinear map f : V → W, where non-degenerate means that Im g contains three non-collinear points. This implies immediately the Fundamental Theorem of projective geometry: Every non-degenerate morphism g between arguesian geometries is described in homogeneous coordinates by a semi-linear map f. For given coordinates f is unique up to a non-zero constant factor. Moreover, the map f is quasilinear if and only if g is a homomorphism.
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© 2000 Springer Science+Business Media Dordrecht
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Faure, CA., Frölicher, A. (2000). Morphisms and Semilinear Maps. In: Modern Projective Geometry. Mathematics and Its Applications, vol 521. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9590-2_10
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DOI: https://doi.org/10.1007/978-94-015-9590-2_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5544-6
Online ISBN: 978-94-015-9590-2
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