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A residue formula for the index of a holomorphic flow. (English) Zbl 0853.32040
Let \(({\mathcal V}, P)\) be a normal, isolated complex singularity, \(\dim {\mathcal V} = n \geq 1\), and \(X\) be a germ of holomorphic vector fields, which is singular only at \(P\). Let \(\widetilde {\mathcal V}\) be a resolution of \(\mathcal V\) and \(\widetilde X\) be the corresponding lifting of \(X\). The authors develop a general approach to the problem of calculation of the Hopf index of \((\widetilde {X}, \widetilde {\mathcal V})\).

MSC:
32S65 Singularities of holomorphic vector fields and foliations
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
32S45 Modifications; resolution of singularities (complex-analytic aspects)
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