La m\'ethode des fa\c{c}ons

TL;DR

The paper introduces a natural method called "la méthode des façons" for stratifying the asymptotic variety associated with a dominant polynomial map, resulting in a differentiable stratification with boundary properties.

Contribution

It presents a new stratification technique for asymptotic varieties of polynomial maps, ensuring differentiability and boundary conditions.

Findings

Provides a differentiable stratification with boundary properties.

Applicable to dominant polynomial maps in complex n-space.

Enhances understanding of asymptotic varieties.

Abstract

Nous donnons une m\'ethode naturelle, que nous appelons {\it "la m\'ethode des fa\c{c}ons"} pour stratifier la vari\'et\'e asymptotique associ\'ee \`a une application polynomiale dominante $F: \mathbb{C}^n \to \mathbb{C}^n$. La stratification obtenue est diff\'erentiable et satisfait la propri\'et\'e de fronti\`ere.