Motivic-type Invariants of Blow-analytic Equivalence

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To a given analytic function germ $f:(\mathbb{R}^d,0) \to (\mathbb{R},0)$, 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.
36 pages, 3 figures

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Algebraic Geometry, 14B05, 32S15, 57R45

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http://salesiana.dossiersoluciones.com/handle/123456789/65812

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0211426
 http://arxiv.org/abs/math/0211426

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arXiv