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| Goulwen Fichou: Motivic invariants of
Arc-Symmetric sets and Blow-Nash Equivalence,
Compositio Math. 141 (2005) 655-688
Abstract: We define invariants of the blow-Nash equivalence of
real analytic function germs, in a similar way that the motivic zeta
functions of Denef \& Loeser. As a key ingredient, we
extend the virtual Betti numbers, which were known for real
algebraic sets, as a generalized Euler characteristic for
projective constructible
arc-symmetric sets. Actually we prove more: the virtual Betti numbers
are not only algebraic invariants, but also Nash invariants of
arc-symmetric sets. Our zeta functions enable to distinguish the blow-Nash
equivalence classes of Brieskorn polynomials of two variables. We
prove moreover that there is no moduli for blow-Nash equivalence in
the case of an algebraic family with isolated singularities.
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