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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-10,
author = {Goulwen Fichou},
title = {Zeta functions and blow-Nash equivalence},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {111-126},
zbl = {1093.14007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-10}
}
Goulwen Fichou. Zeta functions and blow-Nash equivalence. Annales Polonici Mathematici, Tome 85 (2005) pp. 111-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap87-0-10/