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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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References:
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