Massey, David Semi-simple carrousels and the monodromy. (English) Zbl 1102.32013 Ann. Inst. Fourier 56, No. 1, 85-100 (2006). Let \(f: (\mathbb{C}^{n+1},0)\to (\mathbb{C}, 0)\) be a complex analytic germ. If the polar curve \(\Gamma_f\) of \(f\) is irreducible, and the intersection number \((\Gamma_f, V(f))_0\) is prime, then the author obtains strong restriction on the degree \(n\)-cohomology of the Milnor fiber of \(f\). Reviewer: Alexandru Dimca (Nice) Cited in 1 Document MSC: 32S25 Complex surface and hypersurface singularities 32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects) 32S55 Milnor fibration; relations with knot theory Keywords:carrousel; polar curve; monodromy; Milnor fiber PDFBibTeX XMLCite \textit{D. Massey}, Ann. Inst. Fourier 56, No. 1, 85--100 (2006; Zbl 1102.32013) Full Text: DOI arXiv Numdam EuDML References: [1] A’Campo, N., Le nombre de Lefschetz d’une monodromie, Indag. Math., 35, 113-118 (1973) · Zbl 0276.14004 [2] Caubel, C., Variation of the Milnor Fibration in Pencils of Hypersurface Singularities, Proc. London Math. Soc. (3), 83, 330-350 (2001) · Zbl 1022.32010 [3] Lê, D. T., Calcul du Nombre de Cycles Évanouissants d’une Hypersurface Complexe, Ann. Inst. Fourier, Grenoble, 23, 261-270 (1973) · Zbl 0293.32013 [4] Lê, D. T., La Monodromie n’a pas de Points Fixes, J. Fac. Sci. Univ. Tokyo, Sec. 1A, 22, 409-427 (1975) · Zbl 0355.32012 [5] Lê, D. T., The Geometry of the Monodromy Theorem, 8 (1978) · Zbl 0434.32010 [6] Lê, D. T.; Greuel, G.-M., Spitzen, Doppelpunkte und vertikale Tangenten in der Diskriminante verseller Deformationen von vollständigen Durchschnitten, Math. Ann., 222, 71-88 (1976) · Zbl 0318.32015 [7] Lê, D. T.; Massey, D., Hypersurface Singularities and Milnor Equisingularity (2005) · Zbl 1107.32011 [8] Lê, D. T.; Perron, B., Sur la Fibre de Milnor d’une Singularité Isolée en Dimension Complexe Trois, C.R. Acad. Sci., 289, 115-118 (1979) · Zbl 0451.32007 [9] Massey, D., Lê Cycles and Hypersurface Singularities, Lecture Notes in Mathematics, 1615 (1995) · Zbl 0835.32002 [10] Massey, D., The Sebastiani-Thom Isomorphism in the Derived Category, Compos. Math., 125, 353-362 (2001) · Zbl 0986.32004 [11] Massey, D., The Nexus Diagram and Integral Restrictions on the Monodromy (2004) [12] Milnor, J., Singular Points of Complex Hypersurfaces, Annals of Mathematics Studies, 61 (1968) · Zbl 0184.48405 [13] Siersma, D., Isolated Line Singularities, Proc. Symp. Pure Math., 40, 2, 485-496 (1983) · Zbl 0514.32007 [14] Teissier, B., Cycles évanescents, sections planes et conditions de Whitney, Astérisque, 7-8, 285-362 (1973) · Zbl 0295.14003 [15] Tibăr, M., The Lefschetz Number of a Monodromy Transformation (1992) · Zbl 1009.32501 [16] Tibăr, M., Carrousel monodromy and Lefschetz number of Singularities, Enseign. Math. (2), 39, 233-247 (1993) · Zbl 0809.32010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.