[Conditions de non-résonance pour les 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.
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.
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 = {http://archive.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 - http://archive.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 http://archive.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, Tome 53 (2003) no. 6, pp. 1883-1896. doi : 10.5802/aif.1994. http://archive.numdam.org/articles/10.5802/aif.1994/
[1] Hypergeometric Functions, (in Japanese), Springer-Verlag, Tokyo, 1994
[2] Monodromie des systèmes différentiels linéaires à pôles simples sur la sphère de Riemann (d'après A. Bolibruch), Séminaire Bourbaki, Vol. 1992/93 (Astérisque), Volume 216, Exp. No. 765, 4 (1993), pp. 103-119 | EuDML | Numdam | Zbl
[3] Faisceaux Pervers, Analysis and topology on singular spaces, I (Luminy, 1981) (Astérisque), Volume 100 (1982), pp. 5-171 | Zbl
[4] The Riemann-Hilbert problem, Russian Math. Surveys, Volume 45 (1990), pp. 1-58 | DOI | MR | Zbl
[5] On Milnor fibrations of arrangements, J. London Math. Soc., Volume 51 (1995), pp. 105-119 | MR | Zbl
[6] On the number of bounding cycles for nonlinear arrangements, Arrangements--Tokyo 1998 (Adv. Stud. Pure Math), Volume 27 (2000), pp. 51-72 | Zbl
[7] Équations Différentielles à Points Singuliers Réguliers, Lect. Notes in Math., 163, Springer-Verlag, Berlin-New York, 1970 | MR | Zbl
[8] Singularities and Topology of Hypersurfaces, Universitext, Springer-Verlag, New York | MR | Zbl
[9] Sheaves in Topology (Universitext, Springer-Verlag, New York, to appear) | MR | Zbl
[10] Hyperplane arrangements, -tame polynomials and twisted cohomology, Commutative Algebra, Singularities and Computer Algebra (NATO Science Series), Volume Vol. 115 (2003), pp. 113-126 | Zbl
[11] Hypersurface complements, Alexander modules and monodromy (2002) Proceedings of the 7th Workshop on Real and Complex Singularities (Sao Carlos, 2002), to appear, preprint, math.AG/0201291 | MR | Zbl
[12] Equivariant chain complexes, twisted homology and relative minimality of arrangements (2003) (e-print, math.AG/0305266) | Numdam | MR
[13] Cohomology of local systems on the complement of hyperplanes, Invent. Math., Volume 109 (1992), pp. 557-561 | DOI | MR | Zbl
[13] Erratum: "Cohomology of local systems on the complement of hyperplanes", Invent. Math, Volume 112 (1993) no. 2, pp. 447 | MR | Zbl
[14] Logarithmic de Rham complexes and vanishing theorems, Invent. Math., Volume 86 (1986), pp. 161-194 | DOI | MR | Zbl
[15] General theory of hypergeometric functions, Soviet Math. Dokl., Volume 33 (1986) | MR | Zbl
[16] Sheaves on Manifolds, Grundlehren Math. Wiss., 292, Springer-Verlag, Berlin, 1994 | MR | Zbl
[17] Homology of a local system on the complement of hyperplanes, Proc. Japan Acad., Ser. A, Volume 62 (1986), pp. 144-147 | DOI | MR | Zbl
[18] Regular linear systems on and their monodromy groups, Complex analytic methods in dynamical systems (Rio de Janeiro, 1992) (Astérisque), Volume No 222 (1994), pp. 259-283 | Zbl
[19] The topology of complements to hypersurfaces and nonvanishing of a twisted de Rham cohomology, Singularities and complex geometry (Beijing, 1994) (AMS/IP Stud. Adv. Math.), Volume 5 (1997), pp. 116-130 | Zbl
[20] Eigenvalues for the monodromy of the Milnor fibers of arrangements, Trends in Singularities (Trends Math.) (2002), pp. 141-150 | Zbl
[21] Perversity, duality and arrangements in , Topology Appl., Volume 73 (1996), pp. 169-179 | DOI | MR | Zbl
[22] Arrangements of Hyperplanes, Grundlehren Math. Wiss., vol. 300, Springer-Verlag, Berlin | MR | Zbl
[23] Arrangements and Hypergeometric Integrals, MSJ Mem., 9, Math. Soc. Japan, Tokyo, 2001 | MR | Zbl
[24] Local systems over complements of hyperplanes and the Kac-Kazhdan condition for singular vectors, J. Pure Appl. Algebra, Volume 100 (1995), pp. 93-102 | DOI | MR | Zbl
[25] Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups, Adv. Ser. Math. Phys., 21, World Scientific, River Edge, 1995 | MR | Zbl
[26] Cohomology of the Brieskorn-Orlik-Solomon algebras, Comm. Algebra, Volume 23 (1995), pp. 5339-5354 | DOI | MR | Zbl
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