A residue formula for the index of a holomorphic flow (Q1914721)

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 \((\widetilde {X}, \widetilde {\mathcal V})\).