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

Bruce, J. W.

Bull. Lond. Math. Soc. 17, 257-262 (1985).

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

MSC:

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

Keywords:

singular hypersurface germ; versal unfolding; discriminant variety; bifurcation variety; logarithmic vector fields

Citations:

Zbl 0507.32013; Zbl 0497.32016