The \(n\)-dimensional complex projective space \(\mathbb{C}\mathbb{P}^n\) consists of all one-dimensional subspaces of \(\mathbb{C}^{n+1}\). It is a quotient space induced by \(q\colon \mathbb{C}^{n+1}\setminus \{0\}\to \mathbb{C}\mathbb{P}^n\).

Remark
  • The complex projective space is a compact \( 2n \)-manifold (cf. (0x68f51e46) )