An effective study of polynomial maps

摘要

In this paper, using an effective algorithm, we obtain an equivalent statement to the Jacobian Conjecture. For a polynomial map F on an affine space of dimension n over a field of characteristic 0, we define recursively a finite sequence of polynomial maps. We give an equivalent condition to the invertibility of F as well as a formula for F-1 in terms of this finite sequence of polynomial maps. Some examples illustrate the effective aspects of our approach.