Nonresonance conditions for arrangements
Annales de l'Institut Fourier, Volume 53 (2003) no. 6, pp. 1883-1896.

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.

DOI: 10.5802/aif.1994
Classification: 32S22,  53C35,  55N25
Keywords: hyperplane arrangement, local system, Milnor fiber
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, Volume 53 (2003) no. 6, pp. 1883-1896. doi : 10.5802/aif.1994. http://www.numdam.org/articles/10.5802/aif.1994/

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