Blow-Nash types of simple singularities

Goulwen Fichou (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We address the question of the classification under blow-Nash equivalence of simple Nash function germs. We state that this classification coincides with the real analytic classification. We prove moreover that a simple germ can not be blow-Nash equivalent to a nonsimple one. The method is based on the computation of relevant coefficients of the real zeta functions associated to a Nash germ via motivic integration.

Mots clés: Blow-Nash equivalence; Simple singularities; Virtual Poincaré polynomial

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou. Blow-Nash types of simple singularities. Journal of the Mathematical Society of Japan, 2008, 60 (2), pp.445-470. ⟨hal-00132982⟩