On the equivariant blow-Nash classification of simple invariant Nash germs

TL;DR

This paper advances the classification of simple invariant Nash germs under involution using equivariant blow-Nash equivalence and introduces invariants like equivariant zeta functions for this purpose.

Contribution

It provides new insights into classifying invariant Nash germs with involution by employing equivariant zeta functions as invariants.

Findings

Progress in classifying simple invariant Nash germs under involution.

Introduction of equivariant zeta functions as invariants.

Enhanced understanding of equivariant blow-Nash equivalence.

Abstract

We make progress towards the classification of simple Nash germs invariant under the involution changing the sign of the first coordinate, with respect to equivariant blow-Nash equivalence, which is an equivariant Nash version of blow-analytic equivalence, taking advantage of invariants for this relation, the equivariant zeta functions.