Zeta functions and blow-Nash equivalence

Goulwen Fichou. "Zeta functions and blow-Nash equivalence." Annales Polonici Mathematici 87.1 (2005): 111-126. <http://eudml.org/doc/280683>.

@article{GoulwenFichou2005,
abstract = {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.},
author = {Goulwen Fichou},
journal = {Annales Polonici Mathematici},
keywords = {blow-Nash equivalence; zeta function; arc-symmetric set},
language = {eng},
number = {1},
pages = {111-126},
title = {Zeta functions and blow-Nash equivalence},
url = {http://eudml.org/doc/280683},
volume = {87},
year = {2005},
}

TY - JOUR
AU - Goulwen Fichou
TI - Zeta functions and blow-Nash equivalence
JO - Annales Polonici Mathematici
PY - 2005
VL - 87
IS - 1
SP - 111
EP - 126
AB - 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.
LA - eng
KW - blow-Nash equivalence; zeta function; arc-symmetric set
UR - http://eudml.org/doc/280683
ER -