projective line

Projective geometry

• A projective line in P²( R ), consists of the projective points defined by coplanar directions in R ³. In other words, just as the points in P²( R ) correspond to one-dimensional subspaces in R ³, the projective lines correspond to two-dimensional subspaces in R ³.2007, Unnamed translator, Ana Irene Ramírez Galarza, José Seade, Introduction to Classical Geometries, [2002, Introducciòn a la Geometria Avanzada], Springer (Birkhäuser), page 97, In P2( R ), the projective lines are defined by two projective points, that is, by two linearly independent directions of R ³; if we take one vector for each direction, the two vectors generate a plane through the origin in R ³, that is, a subspace of dimension 2, and a projective line can be defined as follows
• 2008, Catriona Maclean (translator), Daniel Perrin, Algebraic Geometry: An Introduction, [1995, D. Perrin, Géométrie algébrique] Springer, page 37, Consider the projective line mathbf P¹, with homogeneous coordinates x and t and open sets U_0(x ne 0) and U_1(t ne 0).