# complex projective line

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

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

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

Title complex projective line ComplexProjectiveLine 2013-03-22 13:59:54 2013-03-22 13:59:54 bwebste (988) bwebste (988) 7 bwebste (988) Definition msc 08B30