This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees) and the notion of essential coordinate components.
Ce travail est un version étendue du cours donné en Juin 2012 à Pau dans le cadre de l’École Arrangements in Pyrénées. School on hyperplane arrangements and related topics. Dans la première partie, nous rappelons comment calculer le groupe fondamental du complément d’un arrangement de droites. La deuxième partie est consacrée aux variétés caractéristiques des arrangements de droites. Deux aspects sont étudiés : la relation avec la position des points singuliers (par rapport aux courbes projectives pour certains degrés fixés) et la notion de composantes coordonnées essentielles.
@article{AFST_2014_6_23_2_223_0,
author = {Enrique Artal Bartolo},
title = {Topology of arrangements and position of singularities},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {223--265},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {2},
year = {2014},
doi = {10.5802/afst.1406},
mrnumber = {3205593},
zbl = {06297892},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1406/}
}
TY - JOUR AU - Enrique Artal Bartolo TI - Topology of arrangements and position of singularities JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 223 EP - 265 VL - 23 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1406/ DO - 10.5802/afst.1406 LA - en ID - AFST_2014_6_23_2_223_0 ER -
%0 Journal Article %A Enrique Artal Bartolo %T Topology of arrangements and position of singularities %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 223-265 %V 23 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1406/ %R 10.5802/afst.1406 %G en %F AFST_2014_6_23_2_223_0
Enrique Artal Bartolo. Topology of arrangements and position of singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 223-265. doi : 10.5802/afst.1406. https://afst.centre-mersenne.org/articles/10.5802/afst.1406/
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