Zeta functions and blow-Nash equivalence

Volume 87 / 2005

Goulwen Fichou Annales Polonici Mathematici 87 (2005), 111-126 MSC: 14B05, 14P20, 14P25, 32S15. DOI: 10.4064/ap87-0-10


We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which has been introduced in [2] as an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo [13]. The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. But though the zeta functions constructed in [2] are no longer invariants for this new relation, thanks to a Denef & Loeser formula coming from motivic integration in a Nash setting, we manage to derive new invariants for this equivalence relation.


  • Goulwen FichouInstitut Mathématiques de Rennes
    Université de Rennes 1
    Campus de Beaulieu
    35042 Rennes Cedex, France

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