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Residues for holomorphic foliations of singular pairs. (English) Zbl 1074.32009

Let \(X\) be a (possibly singular) subvariety of a complex manifold \(M\). Assume that \(Y\) is the intersection of \(X\) with a submanifold \(P\subset M\) and that this intersection is generically transversal. Assume further that there exists a holomorphic foliation \(\mathcal F\) of \(X\) leaving \(Y\) invariant.
The authors prove a type of Camacho-Sad residue theorem for the pair \((X,Y)\).

MSC:

32S65 Singularities of holomorphic vector fields and foliations
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