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Translated tori in the characteristic varieties of complex hyperplane arrangements

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: A.I. Suciu

Editorial: Topology and its Applications, 118 (1-2), p.209-223, 2002.


We give examples of complex hyperplane arrangements A for which the top characteristic variety, V_1(A), contains positive-dimensional irreducible components that do not pass through the origin of the algebraic torus (C^*)^{|A|}. 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.

Cuvinte cheie: hyperplane arrangement; characteristic variety; Orlik-Solomon algebra; translated tori // Hyperplane arrangement, fundamental group, characteristic varieties