Translated tori in the characteristic varieties of complex hyperplane arrangements
Abstract
Description
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.
Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Applications
Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Applications