Diagonalization of nondiagonalizable discrete holomorphic dynamical systems

We shall describe a canonical procedure to associate to any (germ of) holomorphic self-map F of C-n fixing the origin so that dF(O) is invertible and nondiagonalizable an n-dimensional complex manifold M, a holomorphic map pi: M --> C-n, a point e is an element of M and a (germ of) holomorphic self-map (F) over tilde of M such that: pi restricted to M \ pi(-1)(O) is a biholomorphism between M \ pi(-1)(O) and C-n \{O}; pi o (F) over tilde = Fo pi; and e is a fixed point of (F) over tilde such that d (F) over tilde(e) is diagonalizable. Furthermore, we shall use this construction to describe the local dynamics of such an F nearby me origin when sp (dF(O)) = {1}.