For non-dicritical complex hyperbolic foliations in any dimension, every connected component of the exceptional divisor minus the nodal separator set is met by the strict transform of an invariant hypersurface, and s separator blocks split the divisor into exactly s+1 components.
Annales de l’Institut Fourier, 42, 1-2, (1992), 49-72
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Invariant Hypersurfaces and Nodal Components of Foliations
For non-dicritical complex hyperbolic foliations in any dimension, every connected component of the exceptional divisor minus the nodal separator set is met by the strict transform of an invariant hypersurface, and s separator blocks split the divisor into exactly s+1 components.