Publications de Goulwen FICHOU

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.

Charger le

Dernière modification: le 6 juin 2004