Vector fields on discriminants and bifurcation varieties. (English) Zbl 0584.32015

Let f: (\({\mathbb{C}}^ n,0)\to ({\mathbb{C}},0)\) be a holomorphic map germ and B the associated full bifurcation variety. One knows that B is a hypersurface germ, and a result of H. Terao in Math. Ann. 263, 313- 321 (1983; Zbl 0497.32016) states that the module of logarithmic vector fields tangent to B is free over the ring of holomorphic functions on B. The aim of the paper is to give an algorithm to obtain explicit generators of this module and to point out consequences of this algorithm.
Reviewer: C.Banica


32S05 Local complex singularities
32B10 Germs of analytic sets, local parametrization
37G99 Local and nonlocal bifurcation theory for dynamical systems
32S30 Deformations of complex singularities; vanishing cycles
32Sxx Complex singularities
14J17 Singularities of surfaces or higher-dimensional varieties
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