%0 Journal Article
%T Equivariant zeta functions for invariant Nash germs
%+ Institut de Mathématiques de Marseille (I2M)
%+ Department of Mathematics, Faculty of Science, Saitama University
%A Priziac, Fabien
%< avec comité de lecture
%@ 0027-7630
%J Nagoya Mathematical Journal
%I Duke University Press
%V 222
%N 01
%P pp 100 - 136
%8 2016-06
%D 2016
%Z 1403.1020
%R 10.1017/nmj.2016.12
%K Nash germs
%K group action
%K blow-Nash equivalence
%K zeta functions
%K equivariant virtual Poincaré series
%K Denef-Loeser formula
%Z 2010 Mathematics Subject Classification : 14B05, 14P20, 14P25, 32S15, 57S17, 57S25.
%Z Mathematics [math]/Algebraic Geometry [math.AG]Journal articles
%X 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 Poincaré 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.
%G English
%2 https://hal.science/hal-00955670v2/document
%2 https://hal.science/hal-00955670v2/file/eqzetafcts-fpriziac.pdf
%L hal-00955670
%U https://hal.science/hal-00955670
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-