Vector Fields on Discriminants and Bifurcation Varieties
Copyright policy )Vector Fields on Discriminants and Bifurcation Varieties
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 \textit{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.
- Newcastle University United Kingdom
- University of Newcastle Australia Australia
- Edge Hill University United Kingdom
Germs of analytic sets, local parametrization, Local complex singularities, Deformations of complex singularities; vanishing cycles, versal unfolding, Complex singularities, discriminant variety, Local and nonlocal bifurcation theory for dynamical systems, QA Mathematics, bifurcation variety, Singularities of surfaces or higher-dimensional varieties, singular hypersurface germ, logarithmic vector fields
Germs of analytic sets, local parametrization, Local complex singularities, Deformations of complex singularities; vanishing cycles, versal unfolding, Complex singularities, discriminant variety, Local and nonlocal bifurcation theory for dynamical systems, QA Mathematics, bifurcation variety, Singularities of surfaces or higher-dimensional varieties, singular hypersurface germ, logarithmic vector fields
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