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

Krzysztof Kurdyka (1) , Adam Parusinski (2)

1 LAMA - Laboratoire de Mathématiques
2 LJAD - Laboratoire Jean Alexandre Dieudonné

In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. Recall that a function is called arc-analytic if it is real analytic on each real analytic arc. 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: Géométrie algébrique [math.AG]

Krzysztof Kurdyka, Adam Parusinski. On the non-analyticity locus of an arc-analytic function. Journal of Algebraic Geometry, 2012, 21, pp.61-75. ⟨10.1090/S1056-3911-2011-00553-5⟩. ⟨hal-00941026⟩