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

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Date
2009-02-21MFO Scientific Program
Research in Pairs 2008Series
Oberwolfach Preprints;2009,03Author
Kurdyka, Krzysztof
Parusinski, Adam
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Show full item recordOWP-2009-03
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.