complex projective line

Let $ℂ$ be the set of complex numbers. We define an equivalence relation on ${ℂ}^2-\{0,0\}$ by

$$(x1,y1)\sim (x2,y2)\iff \exists \lambda \in {ℂ}^{*}\lambda (x1,y1)=(x2,y2)$$ (1)

The set ${ℂ}^2-\{0,0\}/\sim$ is a projective variety called the complex projective line.

Title	complex projective line
Canonical name	ComplexProjectiveLine
Date of creation	2013-03-22 13:59:54
Last modified on	2013-03-22 13:59:54
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	7
Author	bwebste (988)
Entry type	Definition
Classification	msc 08B30