# complex projective line

Let $\u2102$ be the set of complex numbers. We define an equivalence relation^{} on ${\u2102}^{2}-\{0,0\}$ by

$$(x1,y1)\sim (x2,y2)\iff \exists \lambda \in {\u2102}^{*}\lambda (x1,y1)=(x2,y2)$$ | (1) |

The set ${\u2102}^{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 |