Translated tori in the characteristic varieties of complex hyperplane arrangements

Details Translated tori in the characteristic varieties of complex hyperplane arrangements Translated tori in the characteristic varieties of complex hyperplane arrangements

1999-12-29

arxiv.org/abs/math/9912227v3

Topology and Appl. 118 (2002), 209-223

Mathematics

Algebraic Geometry

Revised and expanded; 16 pages, 10 figures; to appear in Topology and its Applications

Scientific paper

10.1016/S0166-8641(01)00052-9

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.

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