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Given a real polynomial function and a point in its zero locus, we defined a set consisting of algebraic real Puiseux series naturally attached to these data. We prove that this set determines the topology and the geometry of the real Milnor fibre of the function at this point. To achieve this goal, we balance between the tameness properties of this set of Puiseux series, considered as a real algebraic object over the field of algebraic Puiseux series, and its behavior as an infinite dimensional object over the real numbers.
On associe à un zéro d'une fonction polynomiale réelle, un ensemble de séries de Puiseux algébriques. Cet ensemble détermine à la fois la topologie et la géométrie des fibres de Milnor de la fonction en ce point. Pour démontrer cela, on combine les propriétés de modération de cet ensemble de séries de Puiseux, considéré comme un objet de la géométrie réelle sur le corps des séries de Puiseux algébriques, avec son comportement en tant qu'espace de dimension infini sur le corps des nombres réels.
@article{ASENS_2017__50_5_1205_0,
author = {Fichou, Goulwen and Shiota, Masahiro},
title = {Real {Milnor} {Fibres} and {Puiseux} {Series}},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {1205--1240},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 50},
number = {5},
year = {2017},
doi = {10.24033/asens.2343},
mrnumber = {3720028},
zbl = {1386.14199},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.24033/asens.2343/}
}
TY - JOUR AU - Fichou, Goulwen AU - Shiota, Masahiro TI - Real Milnor Fibres and Puiseux Series JO - Annales scientifiques de l'École Normale Supérieure PY - 2017 SP - 1205 EP - 1240 VL - 50 IS - 5 PB - Société Mathématique de France. Tous droits réservés UR - http://geodesic.mathdoc.fr/articles/10.24033/asens.2343/ DO - 10.24033/asens.2343 LA - en ID - ASENS_2017__50_5_1205_0 ER -
%0 Journal Article %A Fichou, Goulwen %A Shiota, Masahiro %T Real Milnor Fibres and Puiseux Series %J Annales scientifiques de l'École Normale Supérieure %D 2017 %P 1205-1240 %V 50 %N 5 %I Société Mathématique de France. Tous droits réservés %U http://geodesic.mathdoc.fr/articles/10.24033/asens.2343/ %R 10.24033/asens.2343 %G en %F ASENS_2017__50_5_1205_0
Fichou, Goulwen; Shiota, Masahiro. Real Milnor Fibres and Puiseux Series. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 50 (2017) no. 5, pp. 1205-1240. doi : 10.24033/asens.2343. http://geodesic.mathdoc.fr/articles/10.24033/asens.2343/
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