[Note sur la conjecture de la monodromie pour une courbe d’espace monomiale dont le semi-groupe est celui d’une branche plane]
En gros, la conjecture de la monodromie pour une singularité dit que chaque pôle de sa fonction zêta d’Igusa motivique induit une valeur propre de sa monodromie. Dans cette note, nous déterminons la fonction zêta d’Igusa motivique ainsi que les valeurs propres de la monodromie pour une courbe d’espace monomiale qui apparaît comme fibre spéciale d’une famille équisingulière dont la fibre générique est une branche plane. En particulier, il en résulte une démonstration de la conjecture de la monodromie pour une telle courbe.
Roughly speaking, the monodromy conjecture for a singularity states that every pole of its motivic Igusa zeta function induces an eigenvalue of its monodromy. In this note, we determine both the motivic Igusa zeta function and the eigenvalues of monodromy for a space monomial curve that appears as the special fiber of an equisingular family whose generic fiber is a plane branch. In particular, this yields a proof of the monodromy conjecture for such a curve.
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@article{CRMATH_2020__358_2_177_0,
author = {Mart{\'\i}n-Morales, Jorge and Mourtada, Hussein and Veys, Willem and Vos, Lena},
title = {Note on the monodromy conjecture for a space monomial curve with a plane semigroup},
journal = {Comptes Rendus. Math\'ematique},
pages = {177--187},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {2},
year = {2020},
doi = {10.5802/crmath.30},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.30/}
}
TY - JOUR AU - Martín-Morales, Jorge AU - Mourtada, Hussein AU - Veys, Willem AU - Vos, Lena TI - Note on the monodromy conjecture for a space monomial curve with a plane semigroup JO - Comptes Rendus. Mathématique PY - 2020 SP - 177 EP - 187 VL - 358 IS - 2 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.30/ DO - 10.5802/crmath.30 LA - en ID - CRMATH_2020__358_2_177_0 ER -
%0 Journal Article %A Martín-Morales, Jorge %A Mourtada, Hussein %A Veys, Willem %A Vos, Lena %T Note on the monodromy conjecture for a space monomial curve with a plane semigroup %J Comptes Rendus. Mathématique %D 2020 %P 177-187 %V 358 %N 2 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.30/ %R 10.5802/crmath.30 %G en %F CRMATH_2020__358_2_177_0
Martín-Morales, Jorge; Mourtada, Hussein; Veys, Willem; Vos, Lena. Note on the monodromy conjecture for a space monomial curve with a plane semigroup. Comptes Rendus. Mathématique, Tome 358 (2020) no. 2, pp. 177-187. doi : 10.5802/crmath.30. http://www.numdam.org/articles/10.5802/crmath.30/
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