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arXiv · 0903.2368

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

Krzysztof Kurdyka·Adam Parusinski
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Abstract

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.

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Krzysztof Kurdyka, Adam Parusinski. 2009-03-13. On the non-analyticity locus of an arc-analytic function. https://arxiv.org/abs/0903.2368

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