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.
Classification: 32S22, 53C35, 55N25
Keywords: hyperplane arrangement, local system, Milnor fiber
@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},
publisher = {Association des Annales de l'institut Fourier},
volume = {53},
number = {6},
year = {2003},
pages = {1883-1896},
doi = {10.5802/aif.1994},
zbl = {1054.32016},
mrnumber = {2038782},
language = {en},
url = {http://www.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, Volume 53 (2003) no. 6, pp. 1883-1896. doi : 10.5802/aif.1994. http://www.numdam.org/item/AIF_2003__53_6_1883_0/
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