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.
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.
Keywords: hyperplane arrangement, local system, Milnor fiber
Mot clés : arrangement d'hyperplans, système local, fibre de Milnor
@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},
mrnumber = {2038782},
zbl = {1054.32016},
language = {en},
url = {https://www.numdam.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://www.numdam.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://www.numdam.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, Volume 53 (2003) no. 6, pp. 1883-1896. doi : 10.5802/aif.1994. https://www.numdam.org/articles/10.5802/aif.1994/
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