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Monodromy. (English) Zbl 1101.14012
Lossen, Christoph (ed.) et al., Singularities and computer algebra. Selected papers of the conference, Kaiserslautern, Germany, October 18–20, 2004 on the occasion of Gert-Martin Greuel’s 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-68309-2/pbk). London Mathematical Society Lecture Note Series 324, 129-155 (2006).
Summary: Let \((X, x)\) be an isolated complete intersection singularity and let \(f: (X, x)\to(\mathbb{C}, 0)\) be the germ of an analytic function with an isolated singularity at \(x\). An important topological invariant in this situation is the Picard-Lefschetz monodromy operator associated to \(f\). We give a survey on what is known about this operator. In particular, we review methods of computation of the monodromy and its eigenvalues (zeta function), results on the Jordan normal form of it, definition and properties of the spectrum, and the relation between the monodromy and the topology of the singularity.
For the entire collection see [Zbl 1086.14001].

14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
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