 Goulwen Fichou: Motivic invariants of
ArcSymmetric sets and BlowNash Equivalence,
Compositio Math. 141 (2005) 655688
Abstract: We define invariants of the blowNash 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
arcsymmetric sets. Actually we prove more: the virtual Betti numbers
are not only algebraic invariants, but also Nash invariants of
arcsymmetric sets. Our zeta functions enable to distinguish the blowNash
equivalence classes of Brieskorn polynomials of two variables. We
prove moreover that there is no moduli for blowNash equivalence in
the case of an algebraic family with isolated singularities.
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