A new characterization of the invertibility of polynomial maps

2016/01/03 by Adamus, Elzbieta, Bogdan, Pawel, Crespo, Teresa +1
#14R15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.00332

Abstract

In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the invertibility of F as well as a formula for the inverse of F in terms of these finite sequences of polynomials. Some examples illustrate the effective aspects of our approach.

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