An algorithm to classify the asymptotic set associated to a polynomial mapping

Abstract

We provide an algorithm to classify the asymptotic sets of the dominant polynomial mappings $F: \C^3 \to \C^3$ of degree 2, using the definition of the so-called "{\it façons}" in \cite{Thuy}. We obtain a classification theorem for the asymptotic sets of dominant polynomial mappings $F: \C^3 \to \C^3$ of degree 2. This algorithm can be generalized for the dominant polynomial mappings $F: \C^n \to \C^n$ of degree $d$, with any $(n,d)\in {({\mathbb{N}}^{\ast })}^2$.