Motivic-type Invariants of Blow-analytic Equivalence

Details Motivic-type Invariants of Blow-analytic Equivalence Motivic-type Invariants of Blow-analytic Equivalence

2002-11-27

arxiv.org/abs/math/0211426v1

Mathematics

Algebraic Geometry

36 pages, 3 figures

Scientific paper

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.

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