Motivic-type invariants of blow-analytic equivalence

Satoshi Koike[1]; Adam Parusiński[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)

Annales de l'Institut Fourier (2003)

  • Volume: 53, Issue: 7, page 2061-2104
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Koike, Satoshi, and Parusiński, Adam. "Motivic-type invariants of blow-analytic equivalence." Annales de l'Institut Fourier 53.7 (2003): 2061-2104. <http://eudml.org/doc/116094>.

@article{Koike2003,
abstract = {To a given analytic function germ $f:(\{\mathbb \{R\}\}^d,0) \rightarrow (\{\mathbb \{R\}\},0)$, we associate zeta functions $Z_\{f,+\}$, $Z_\{f,-\} \in \{\mathbb \{Z\}\} [[T]]$, 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.},
affiliation = {Hyogo University of Teacher Education, Department of Mathematics, 942-1 Shimokume, Kato, Yashiro, Hyogo 673-1494 (Japon); Université d'Angers, Département de Mathématiques, 2 Bd Lavoisier, 49045 Angers Cedex (France)},
author = {Koike, Satoshi, Parusiński, Adam},
journal = {Annales de l'Institut Fourier},
keywords = {blow-analytic equivalence; motivic integration; zeta functions; Thom-Sebastiani formulae},
language = {eng},
number = {7},
pages = {2061-2104},
publisher = {Association des Annales de l'Institut Fourier},
title = {Motivic-type invariants of blow-analytic equivalence},
url = {http://eudml.org/doc/116094},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Koike, Satoshi
AU - Parusiński, Adam
TI - Motivic-type invariants of blow-analytic equivalence
JO - Annales de l'Institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 7
SP - 2061
EP - 2104
AB - To a given analytic function germ $f:({\mathbb {R}}^d,0) \rightarrow ({\mathbb {R}},0)$, we associate zeta functions $Z_{f,+}$, $Z_{f,-} \in {\mathbb {Z}} [[T]]$, 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.
LA - eng
KW - blow-analytic equivalence; motivic integration; zeta functions; Thom-Sebastiani formulae
UR - http://eudml.org/doc/116094
ER -

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