projective line

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projective line (plural projective lines)

  1. (projective geometry) A line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
    • 2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97,
      In , the projective lines are defined by two projective points, that is, by two linearly independent directions of ; if we take one vector for each direction, the two vectors generate a plane through the origin in , that is, a subspace of dimension 2, and a projective line can be defined as follows:
      A projective line in , consists of the projective points defined by coplanar directions in .
      In other words, just as the points in correspond to one-dimensional subspaces in , the projective lines correspond to two-dimensional subspaces in .
    • 2008, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique] Springer, page 37,
      Consider the projective line , with homogeneous coordinates and and open sets and .
    • 2009, Dirk Kussin, Noncommutative Curves of Genus Zero: Related to Finite Dimensional Algebras, American Mathematical Society, page 13,
      The projective line is related to the Kronecker algebra, [] In general one has to deal with the so-called weighted case which leads to the study of the canonical algebras and to the weighted projective lines (as Ringel pointed out in his survey [93]).


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