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

摘要

We provide an algorithm to classify the asymptotic sets of the dominantpolynomial mappings $F: \C^3 \to \C^3$ of degree 2, using the definition of theso-called "{\it fa\c{c}ons}" in \cite{Thuy}. We obtain a classification theoremfor the asymptotic sets of dominant polynomial mappings $F: \C^3 \to \C^3$ ofdegree 2. This algorithm can be generalized for the dominant polynomialmappings $F: \C^n \to \C^n$ of degree $d$, with any $(n, d) \in {(\N^*)}^2$.