Let V be a complex vector space of dimension \(n+1\ge 2\) . The group \({\mathbb C}_{*}={\mathbb C}\setminus \{0\}\) acts on the open set \(V_{*}=V\setminus \{0\}\) by multiplication: \((\lambda ,z)\rightarrow \lambda z\) , \(\lambda \in {\mathbb C}_{*}\) , \(z\in V_{*}\) . Recall that the quotient topological space \({\mathbb P}(V)=V_{*}/{\mathbb C}_{*}\) is called the projective space of V. Every equivalence class [z] is uniquely determined by a non-zero vector z of V. Every complex line of V (a 1-dimensional complex subspace) is also determined by such a vector. Hence the map \([z]\rightarrow {\mathbb C}.z\) is a bijection of \({\mathbb P}(V)\) onto the set of complex lines of V.