Massey, David B. Intersection cohomology monodromy and the Milnor fiber. (English) Zbl 1183.32009 Int. J. Math. 20, No. 4, 491-507 (2009). A complex analytic space \( X\) is said to be an intersection cohomology manifold if the shifted constant sheaf on \( X\) is isomorphic to the intersection cohomology. Given an analytic function \( f\) on an intersection cohomology manifold, the author describes a simple relation between \( V(f)\) being an intersection cohomology manifold and the vanishing cycle Milnor monodromy of \( f\). He then describes how the Sebastiani-Thom isomorphism allows one to produce intersection cohomology manifolds with arbitrary singular sets. Finally, he obtains restrictions on the cohomology of the Milnor fiber of a hypersurface with a special type of one-dimensional critical locus. Reviewer: Vincent Thilliez (Villeneuve d’Ascq) Cited in 6 Documents MSC: 32C35 Analytic sheaves and cohomology groups 32C18 Topology of analytic spaces 32B15 Analytic subsets of affine space 32B10 Germs of analytic sets, local parametrization Keywords:intersection cohomology; monodromy; Milnor fiber; vanishing cycles PDFBibTeX XMLCite \textit{D. B. Massey}, Int. J. Math. 20, No. 4, 491--507 (2009; Zbl 1183.32009) Full Text: DOI arXiv References: [1] Barlet D., Ann. Sci. École Norm. Sup. (4) 24 pp 401– [2] Beilinson A. A., Astérisque 100 pp 5– [3] Borho W., Astérisque 101 pp 23– [4] DOI: 10.1090/S0002-9904-1978-14527-3 · Zbl 0418.57005 [5] DOI: 10.1090/S0002-9947-1969-0233814-9 [6] DOI: 10.1016/0040-9383(80)90003-8 · Zbl 0448.55004 [7] Goresky M., Invent. Math. 71 pp 77– [8] Goresky M., Astérisque 101 pp 135– [9] Grothendieck A., Lecture Notes in Mathematics 288, in: Séminaire de Géométrie Algébrique (SGA VII-1) (1972) · Zbl 0234.00007 [10] Hamm H., Progress in Mathematics 87 (1990) [11] Kashiwara M., Astérisque 128 pp 235– [12] DOI: 10.1007/978-3-662-02661-8 [13] DOI: 10.1090/S0002-9947-1973-0344248-1 [14] Lê D. T., Ann. Inst. Fourier (Grenoble) 23 pp 261– [15] Lê D. T., Indag. Math. 35 pp 403– [16] D. T. Lê, C. P. Ramanujam – A Tribute, Tata Institute of Fundametal Research Studies in Mathematics 8 (Springer-Verlag, 1978) pp. 157–173. [17] Lê D. T., Pure Appl. Math. Quart. 2 pp 893– [18] DOI: 10.1023/A:1002608716514 · Zbl 0986.32004 [19] Massey D., Mem. Amer. Math. Soc. 778 [20] Milnor J., Annals of Mathematics Studies, in: Singular Points of Complex Hypersurfaces (1968) · Zbl 0184.48405 [21] Némethi A., Compositio Math. 80 pp 1– [22] DOI: 10.2969/jmsj/04320213 · Zbl 0739.32034 [23] DOI: 10.1016/0040-9383(73)90019-0 · Zbl 0263.32005 [24] DOI: 10.2969/jmsj/02640714 · Zbl 0286.32010 [25] Schürmann J., Monografie Matematyczne 63, in: Topology of Singular Spaces and Constructible Sheaves (2004) [26] DOI: 10.1007/BF01390095 · Zbl 0233.32025 [27] DOI: 10.1016/0040-9383(91)90025-Y · Zbl 0746.32014 [28] DOI: 10.2307/1970239 · Zbl 0099.39202 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.