The index of a holomorphic flow with an isolated singularity. (English) Zbl 0725.32012

The index of a holomorphic vector field Z on the germ of a hypersurface \({\mathcal V}\) with an isolated singularity is defined. The index coincides with the Hopf index in the smooth case. Formulae for the index in terms of the ideals defining Z and \({\mathcal V}\) are given. Topological invariance of the index and the Chern class as well as formulae relating global invariants of the Poincaré-Hopf type are proven.
Reviewer: X.Gómez-Mont


32S05 Local complex singularities
32S25 Complex surface and hypersurface singularities
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
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