Meaning of projective line | Babel Free

Definitions

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

Equivalents

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.”

“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).”

“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]).”

CEFR level