Projective Lines, Cross-Ratios, Homographies

Part of the Problem Books in Mathematics book series (PBM)


To any four distinct points (a i ) i = 1,2,3,4 on a projective line (considered by itself or inside a projective space), we associate a scalar, denoted by [a i ] = [a l, a 2, a 3, a 4], and called the cross-ratio of these four points. For points on an affine line D, the cross-ratio is defined to be the same as on the completion \(\tilde D = D \cup {\infty _D}\) (cf. 5.A).


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Copyright information

© Marcel Berger 1984

Authors and Affiliations

  1. 1.U.E.R. de Mathematique et InformatiqueUniversité Paris VIIParis, Cedex 05France
  2. 2.Centre National de la Recherche ScientifiqueParisFrance
  3. 3.P.U.K.GrenobleFrance

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