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

TL;DR

This paper introduces an algorithm for classifying the asymptotic sets of degree 2 polynomial mappings from complex 3-space to itself, with potential generalization to higher dimensions and degrees.

Contribution

It provides a new algorithmic approach to classify asymptotic sets of polynomial mappings, extending previous theoretical results to a practical computational method.

Findings

Classification theorem for degree 2 mappings in  

Algorithmic method for asymptotic set classification

Potential generalization to higher dimensions and degrees

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 fa\c{c}ons}" 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 $(n, d) \in {(\N^*)}^2$.