complex projective line

Noun

 * 1)  A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line);  the set of equivalence classes of ordered pairs (α, β) of complex numbers, not both zero, with respect to the equivalence relation "(α, β) ≡ (λα, λβ) for all nonzero complex λ".

Usage notes

 * The formal definition above is a version of the definition of a projective space by homogeneous coordinates. (See also )
 * Notations include: $$\mathbb{P}(\C^2),\ \mathbb{P}_1(\C)\text{ and } \C\mathbb{P}^1$$.