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The Milnor fiber of a generic arrangement. (English) Zbl 0807.32029
Let \(V\) be the union of \(m\) hyperplanes through the origin of \(\mathbb{C}^ n\) such that \(m > n\) and no \(n\) of these hyperplanes share a line. The authors compute the complex cohomology of the Milnor’s fibre and the characteristic polynomial of the monodromy of the (non-isolated) singularity of \(V\) at the origin.

32S55 Milnor fibration; relations with knot theory
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
Full Text: DOI
[1] Artal-Bartolo, E., Sur le premier nombre de Betti de la fibre de Milnor du cône sur une courbe projective plane et son rapport avec la position des points singuliers,Preprint.
[2] Brieskorn, E., Sur les groupes de tresses, inSéminaire Bourbaki 1971/72, Lecture Notes in Math. 317, pp. 21–44, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
[3] Dimca, A., On the Milnor fibrations of weighted homogeneous polynomials,Preprint. · Zbl 0726.14002
[4] Esnault, H., Fibre de Milnor d’un cône sur une courbe plane singulière,Invent. Math. 68 (1982), 477–496. · Zbl 0489.14009
[5] Hattori, A., Topology of C n minus a finite number of affine hyperplanes in general position,J. Fac. Sci. Tokyo 22 (1975), 205–219. · Zbl 0306.55011
[6] Milnor, J.,Singular Points of Complex Hypersurfaces, Princeton Univ. Press, Princeton, N.J., 1968. · Zbl 0184.48405
[7] Milnor, J. andOrlik, P., Isolated singularities defined by weighted homogeneous polynomials,Topology 9 (1970), 385–393. · Zbl 0204.56503
[8] Orlik, P.,Introduction to Arrangements,CBMS Lecture Notes 72, Amer. Math. Soc., Providence, R.I., 1989. · Zbl 0722.51003
[9] Orlik, P. andSolomon, L., Singularities I: Hypersurfaces with an isolated singularity,Adv. in Math. 27 (1978), 256–272. · Zbl 0369.14002
[10] Randell, R., On the topology of non-isolated singularities, inProceedings of the Georgia Topology Conference 1977, pp. 445–473, Academic Press, New York, 1979.
[11] Siersma, D., Singularities with critical locus a 1-dimensional complete intersection and transversal typeA 1,Topology Appl. 27 (1987), 51–73. · Zbl 0635.32006
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