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Holomorphic vector fields tangent to foliations in dimension three

Holomorphic vector fields tangent to foliations in dimension three

We consider a singular holomorphic vector field in a neighborhood of 0∈ C3and suppose that there is a singular holomorphic foliation of codimension one (outside its singular set, given by a holomorphic decomposition of this neighborhood into complex surfaces, called leaves) to which it is tangent. This means that, when …