Abstract
The quantum deformation CP q (N) of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is studied and CP q (N) appears as a quantum Kähler manifold. The braiding of several copies of CP q (N) is introduced and the anharmonic ratios of four collinear points are shown to be invariant under quantum projective transformations. They provide the building blocks of all projective invariants. The Poisson limit is also described. © 1996 Springer-Verlag.