Motivic invariants of arc-symmetric sets and blow-Nash equivalence. (English) Zbl 1080.14070
The author defines virtual Betti numbers and a virtual Euler characteristic for real constructible arc-symmetric sets, and respectively an analogue of the Denef-Loeser motivic zeta-function, motivic Poincaré polynomial. It is proven that these objects are invariants with respect to the blow-Nash equivalence. As application, the author gives the blow-Nash classification of Brieskorn polynomials in two variables, and also shows that the blow-Nash equivalence in algebraic families with isolated singularities has no moduli.
Reviewer: Eugenii I. Shustin (Tel Aviv)
MSC:
14P20 | Nash functions and manifolds |
14B05 | Singularities in algebraic geometry |
32S15 | Equisingularity (topological and analytic) |
14P25 | Topology of real algebraic varieties |