  We give examples of complex hyperplane arrangements for which the top
characteristic variety contains positive-dimensional irreducible components
that do not pass through the origin of the character torus. These examples
answer several questions of Libgober and Yuzvinsky. As an application, we
exhibit a pair of arrangements for which the resonance varieties of the
Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic
varieties are not isomorphic. The difference comes from translated components,
which are not detected by the tangent cone at the origin.
