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On the dimension of resonance and characteristic varieties

We study codimension one foliations on complex projective spaces Pn associated to nontrivial resonance varieties of (complex projective) hyperplane arrangements. Using methods from theory of foliations we obtain certain upper bounds on the dimensions of those varieties as functions of n. Equivalently this gives upper bounds on the number of completely reducible fibers of pencils of hypersurfaces of Pn. We obtain similar bounds for the dimensions of the characteristic varieties of the arrangement complements.