Equivariant zeta functions for invariant Nash germs (Q2828014)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Equivariant zeta functions for invariant Nash germs |
scientific article; zbMATH DE number 6642614
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equivariant zeta functions for invariant Nash germs |
scientific article; zbMATH DE number 6642614 |
Statements
24 October 2016
0 references
Nash germs
0 references
blow-Nash equivalence
0 references
motivic zeta functions
0 references
equivariant zeta functions
0 references
virtual Poincaré series
0 references
0 references
0 references
0 references
0.8953993
0 references
0.8924594
0 references
0.89202046
0 references
0.8898742
0 references
0.8895248
0 references
0.88822675
0 references
0.8792213
0 references
0 references
0.87223566
0 references
Equivariant zeta functions for invariant Nash germs (English)
0 references
By definition, Nash germs are real analytic germs with semialgebraic graph [\textit{G. Fichou}, Ann. Pol. Math. 87, 111--126 (2005; Zbl 1093.14007)]. The author develops the theory of Nash germs invariant under the right composition with a linear action of a finite group. At first, following [loc.cite] he introduces for such germs a blow-Nash equivalence involving equivariant data. Using the equivariant virtual Poincaré series from \textit{G. Fichou} [Ann. Inst. Fourier 58, No. 1, 1--27 (2008; Zbl 1142.14003)], he then associates to any equivariant Nash germ an equivariant zeta function and proves that it is rational by formulas from \textit{J. Denef} and \textit{F. Loeser} [Invent. Math. 135, No. 1, 201--232 (1999; Zbl 0928.14004)]. Finally, for several invariant Nash germs the equivariant zeta functions are computed explicitly.
0 references
