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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2009
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  • HAL Id : hal-00389210, version 1

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

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