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

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

2009-03-13

arxiv.org/abs/0903.2368v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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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