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.
Classification : 32S22, 53C35, 55N25
Mots 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'institut Fourier},
volume = {53},
number = {6},
year = {2003},
doi = {10.5802/aif.1994},
zbl = {1054.32016},
mrnumber = {2038782},
language = {en},
url = {archive.numdam.org/item/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. http://archive.numdam.org/item/AIF_2003__53_6_1883_0/
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