projective line

plural projective lines

1. projective geometryA line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.

   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).

   2 more examples

   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

   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]).

   2009, Dirk Kussin, Noncommutative Curves of Genus Zero: Related to Finite Dimensional Algebras, American Mathematical Society, page 13

   Synonyms: projective straight line