On some classification results of real singularities up to the arc-analytic equivalence (Singularity theory of differential maps and its applications)

Abstract

This note is an expanded version of a talk given during the conference Singularity theory of differential maps and ifs applications at the RIMS, Kyoto (December 6-9, 2016). We first state the definition and some properties of the arc-analytic equivalence which is an equivalence relation with no continuous moduli on Nash(i.e. real analytic and semialgebraic) function germs. It is a semialgebraic version of the blow-analytic equivalence of T.-C. Kuo. Then, we present an invariant of the arc-analytic equivalence which is constructed following the motivic zeta function of Denef-Loeser. Finally, we explain how to derive from it some classification results for Brieskorn polynomials and more generally for some weighted homogeneous polynomials.