Une stratification de Thom-Mather de lensemble asymptotique dune application polynomial mapping $F: \mathbb{C}^n \to \mathbb{C}^n$

TL;DR

This paper proves that the stratification of the asymptotic set of a polynomial mapping from complex n-space to itself, defined by a specific method, satisfies the Thom-Mather conditions, ensuring a well-behaved geometric structure.

Contribution

It establishes that the stratification of the asymptotic set for such polynomial mappings is a Thom-Mather stratification, confirming its geometric regularity.

Findings

The stratification is a Thom-Mather stratification.

The method applies to polynomial mappings in complex n-space.

Provides a geometric framework for understanding asymptotic sets.

Abstract

We prove that the stratification of the asymptotic set associated to a polynomial mapping $F: \mathbb{C}^n \to \mathbb{C}^n$ defined by "la m\'ethode des fa\c{c}ons" (arXiv:1407.5329) is a Thom-Mather stratification. Nous prouvons que la stratification de lensemble asymptotique dune application polynomial mapping $F: \mathbb{C}^n \to \mathbb{C}^n$ d\'efinie par "la m\'ethode des fa\c{c}ons" (arXiv:1407.5329) est une stratification de Thom-Mather