Motivic invariants of Arc-Symmetric sets and Blow-Nash Equivalence

Goulwen Fichou

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arXiv · math/0304195

Motivic invariants of Arc-Symmetric sets and Blow-Nash Equivalence

Goulwen Fichou

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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 characteristics for projective constructible arc-symmetrics sets. Actually we prove more: the virtual Betti numbers are not only algebraic invariant, but also Nash-invariant of arc-symmetric sets. Our zeta functions enable to sketch the blow-Nash equivalence classes of Brieskorn polynomials of two variables.

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BibTeX RIS

Goulwen Fichou. 2003-04-15. Motivic invariants of Arc-Symmetric sets and Blow-Nash Equivalence. https://arxiv.org/abs/math/0304195

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