[Groupe fondamental du complément de la discriminante des singularités de Brieskorn–Pham]
En cette Note nous rapellons la monodromie de tresses pour le discriminants de singularités d'une hypersurface et nous présentons deux résultats de Lönne (2003) : la monodromie de tresses associée aux singularités de Brieskorn–Pham est donnée par un nombre fini de tresses, et nous en déduisons une très belle présentation finie du groupe fondamental d'un complément d'une discriminante.
In this Note we recall the braid monodromy of discriminants of hypersurface singularities and present two results from Lönne (2003): the braid monodromy associated to hypersurface singularities of Brieskorn–Pham type is given explicitly in terms of finitely many braids, and we show how this leads to very nice finite presentations of fundamental groups of the discriminant complements.
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@article{CRMATH_2007__345_2_93_0,
author = {L\"onne, Michael},
title = {Fundamental group of discriminant complements of {Brieskorn{\textendash}Pham} polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {93--96},
publisher = {Elsevier},
volume = {345},
number = {2},
year = {2007},
doi = {10.1016/j.crma.2007.05.022},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.05.022/}
}
TY - JOUR AU - Lönne, Michael TI - Fundamental group of discriminant complements of Brieskorn–Pham polynomials JO - Comptes Rendus. Mathématique PY - 2007 SP - 93 EP - 96 VL - 345 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.05.022/ DO - 10.1016/j.crma.2007.05.022 LA - en ID - CRMATH_2007__345_2_93_0 ER -
%0 Journal Article %A Lönne, Michael %T Fundamental group of discriminant complements of Brieskorn–Pham polynomials %J Comptes Rendus. Mathématique %D 2007 %P 93-96 %V 345 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.05.022/ %R 10.1016/j.crma.2007.05.022 %G en %F CRMATH_2007__345_2_93_0
Lönne, Michael. Fundamental group of discriminant complements of Brieskorn–Pham polynomials. Comptes Rendus. Mathématique, Tome 345 (2007) no. 2, pp. 93-96. doi : 10.1016/j.crma.2007.05.022. http://www.numdam.org/articles/10.1016/j.crma.2007.05.022/
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