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arXiv · 1403.1020

Equivariant zeta functions for invariant Nash germs

Fabien Priziac
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Abstract

To any Nash germ invariant under right composition with a linear action of a finite group, we associate its equivariant zeta functions, inspired from motivic zeta functions, using the equivariant virtual Poincar\'e series as a motivic measure. We show Denef-Loeser formulae for the equivariant zeta functions and prove that they are invariants for equivariant blow-Nash equivalence via equivariant blow-Nash isomorphisms. Equivariant blow-Nash equivalence between invariant Nash germs is defined as a generalization involving equivariant data of the blow-Nash equivalence.

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Fabien Priziac. 2014-03-05. Equivariant zeta functions for invariant Nash germs. https://doi.org/10.1017/nmj.2016.12

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