Nonresonance conditions for arrangements
[Conditions de non-résonance pour les arrangements]
Annales de l'Institut Fourier, Tome 53 (2003) no. 6, pp. 1883-1896.

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.

DOI : 10.5802/aif.1994
Classification : 32S22, 53C35, 55N25
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

1 Louisiana State University, Department of Mathematics, Baton Rouge LA 70803 (USA)
2 Université Bordeaux I, Laboratoire de Mathématiques Pures, 351 cours de la Libération, 33405 Talence Cedex (France)
3 University of Wisconsin, Department of Mathematics, Madison WI 53706 (USA)
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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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