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

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)
Full Text: