Variation mappings on singularities with a 1-dimensional critical locus. (English) Zbl 0746.32014

Siersma, Dirk

Topology 30, No. 3, 445-469 (1991).

Let \(f:(\mathbb{C}^{n+1},0)\to(\mathbb{C},0)\) be a germ of an analytic function with a 1-dimensional singular locus \(\sigma=\sigma_ 1\cup\dots\cup\sigma_ r\), \(\sigma_ i\) irreducible curves. Let \(F\) be the Milnor fibre of \(f\) and \(F_ i\) the Milnor fibres of the germ of a generic transversal section at \(x\in\sigma_ i\setminus\{0\}\). This way one obtains several monodromy actions on the corresponding homology group. The aim of the paper is to study these monodromies to understand the topology of this class of singularities.

Reviewer: G.Pfister (Berlin)

MSC:

32S55	Milnor fibration; relations with knot theory
14B05	Singularities in algebraic geometry
32S40	Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)

Keywords:

line singularities; Milnor fibration; topology singularities; monodromy