no. 7
Motivic-type invariants of blow-analytic equivalence
Koike, Satoshi1; Parusiński, Adam2
1 Hyogo University of Teacher Education, Department of Mathematics, 942-1 Shimokume, Kato, Yashiro, Hyogo 673-1494 (Japon)
2 Université d'Angers, Département de Mathématiques, 2 Bd Lavoisier, 49045 Angers Cedex (France)
Annales de l'Institut Fourier, Volume 53 (2003) no. 7, pp. 2061-2104.

To a given analytic function germ f:(ℝ d ,0)→(ℝ,0), we associate zeta functions Z f,+ , Z f,- ∈ℤ[[T]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic equivalence classes of Brieskorn polynomials of three variables.

Soit f:(ℝ d ,0)→(ℝ,0) un germe de fonction analytique. On associe à f des fonctions zêta Z f,+ , Z f,- ∈ℤ[[T]] définies de manière similaire aux fonctions zêta motiviques de Denef et Loeser. On montre que ces fonctions sont rationnelles et ne dépendent que de la classe d’équivalence blow-analytique au sens de Kuo de f. En utilisant ces fonctions zêta et l’invariant de Fukui on donne une classification des polynômes de Brieskorn de deux variables à équivalence blow-analytique près. Pour les polynômes de Brieskorn de trois variables on obtient une classification presque complète.

DOI: 10.5802/aif.2001
Classification: 14B05, 32S15
Keywords: blow-analytic equivalence, motivic integration, zeta functions, Thom-Sebastiani formulae
Koike, Satoshi 1; Parusiński, Adam 2

1 Hyogo University of Teacher Education, Department of Mathematics, 942-1 Shimokume, Kato, Yashiro, Hyogo 673-1494 (Japon)
2 Université d'Angers, Département de Mathématiques, 2 Bd Lavoisier, 49045 Angers Cedex (France) 
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Koike, Satoshi; Parusiński, Adam. Motivic-type invariants of blow-analytic equivalence. Annales de l'Institut Fourier, Volume 53 (2003) no. 7, pp. 2061-2104. doi : 10.5802/aif.2001. https://aif.centre-mersenne.org/articles/10.5802/aif.2001/

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