On almost Blow-analytic equivalence

Goulwen Fichou (1) , Masahiro Shiota (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematics [Nagoya]

Approximation of real analytic functions by Nash functions is a classical topic in real geometry. In this paper, we focus on the Nash approximation of an analytic desingularization of a Nash function germ obtained by a sequence of blowings-up along smooth analytic centers. We apply the result to prove that Nash function germs that are analytically equivalent after analytic desingularizations are Nash equivalent after Nash desingularizations. Results are based on a precise Euclidean description of a sequence of blowings-up combined with Néron Desingularization.

Mots clés: Real analytic functions; Nash functions; desingularization

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Masahiro Shiota. On almost Blow-analytic equivalence. 2010. ⟨hal-00346718v1⟩