On the non-analyticity locus of an arc-analytic function

Krzysztof Kurdyka (1) , Adam Parusinski (2)

1 LAMA - Laboratoire de Mathématiques
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

A function is called arc-analytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arc-analytic functions that are not real analytic. Arc analytic functions appear while studying the arc-symmetric sets and the blow-analytic equivalence. In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. We discuss also the behavior of the non-analyticity locus under blowings-up. By a result of Bierstone and Milman a big class of arc-analytic function, namely those that satisfy a polynomial equation with real analytic coefficients, can be made analytic by a sequence of global blowings-up with smooth centers. We show that these centers can be chosen, at each stage of the resolution, inside the non-analyticity locus.

Domaines: Topologie géométrique [math.GT]

Krzysztof Kurdyka, Adam Parusinski. On the non-analyticity locus of an arc-analytic function. 2009. ⟨hal-00389210⟩