From the blow-analytic equivalence to the arc-analytic equivalence: a survey
Résumé
In the early eighties T.-C. Kuo introduced the blow-analytic equivalence in order to obtain a classification of real analytic function germs with no continuous moduli.
This new notion has been subsequently extensively investigated. In particular it led to the blow-Nash equivalence of G. Fichou and more recently to the arc-analytic equivalence. These notions may be seen as algebraic versions of the blow-analytic equivalence in order to classify Nash function germs with no continuous moduli.
This survey aims to give a self-contained introduction to this topic. It focuses on the construction of invariants of the above cited relations. In order to introduce some of these invariants, it is necessary to briefly recall some notions of motivic integration.