[Conditions de non-résonance pour les arrangements]
Nous démontrons un théorème d'annulation pour la cohomologie du complémentaire d'un arrangement d'hyperplans complexes à coefficients dans un système local. Ce résultat est comparé à d'autres théorèmes d'annulation et il est utilisé pour étudier les fibres de Milnor associées à des arrangements de droites et d'hypersurfaces.
We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.
Keywords: hyperplane arrangement, local system, Milnor fiber
Mot clés : arrangement d'hyperplans, système local, fibre de Milnor
Cohen, Daniel C. 1 ; Dimca, Alexandru 2 ; Orlik, Peter 3
@article{AIF_2003__53_6_1883_0,
author = {Cohen, Daniel C. and Dimca, Alexandru and Orlik, Peter},
title = {Nonresonance conditions for arrangements},
journal = {Annales de l'Institut Fourier},
pages = {1883--1896},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {53},
number = {6},
year = {2003},
doi = {10.5802/aif.1994},
zbl = {1054.32016},
mrnumber = {2038782},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1994/}
}
TY - JOUR AU - Cohen, Daniel C. AU - Dimca, Alexandru AU - Orlik, Peter TI - Nonresonance conditions for arrangements JO - Annales de l'Institut Fourier PY - 2003 SP - 1883 EP - 1896 VL - 53 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1994/ DO - 10.5802/aif.1994 LA - en ID - AIF_2003__53_6_1883_0 ER -
%0 Journal Article %A Cohen, Daniel C. %A Dimca, Alexandru %A Orlik, Peter %T Nonresonance conditions for arrangements %J Annales de l'Institut Fourier %D 2003 %P 1883-1896 %V 53 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1994/ %R 10.5802/aif.1994 %G en %F AIF_2003__53_6_1883_0
Cohen, Daniel C.; Dimca, Alexandru; Orlik, Peter. Nonresonance conditions for arrangements. Annales de l'Institut Fourier, Tome 53 (2003) no. 6, pp. 1883-1896. doi : 10.5802/aif.1994. https://aif.centre-mersenne.org/articles/10.5802/aif.1994/
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