nLab
complex line

Contents

Idea

A complex line is a complex vector space of dimension 1 (of complex dimension that is, as a \mathbb{C}-vector space, meaning that as a vector space over the real numbers it is a plane).

In particular the complex plane \mathbb{C} itself is a complex line; conversely, any two complex lines are isomorphic (to each other and to the complex plane). However, there are many such isomorphisms; the automorphism group is {0}\mathbb{C} \setminus \{0\}.

Revised on May 14, 2014 02:25:16 by Urs Schreiber (77.251.114.72)