Characteristic varieties of arrangements

dc.creatorCohen, Daniel C.
dc.creatorSuciu, Alexander I.
dc.date1998-01-11
dc.date1998-04-11
dc.date.accessioned2026-07-07T05:23:33Z
dc.date.available2026-07-07T05:23:33Z
dc.descriptionThe k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of V_k(A). For any arrangement A, we show that the tangent cone at the identity of this variety coincides with R^1_k(A), one of the cohomology support loci of the Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all positive-dimensional components of V_k(A) are combinatorially determined, and that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving a conjecture of Falk. We use these results to study the reflection arrangements associated to monomial groups.
dc.descriptionLaTeX2e, 20 pages. A reference to Libgober's recent work in math.AG/9801070 is added. Several points are clarified, a new example is included
dc.identifierhttps://arxiv.org/abs/math/9801048
dc.identifierhttp://arxiv.org/abs/math/9801048
dc.identifierMathematical Proceedings of the Cambridge Philosophical Society 127 (1999), no. 1, 33-53
dc.identifierdoi:10.1017/S0305004199003576
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76483
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subject14M12, 52B30 (Primary); 14H30, 20F36, 57M05 (Secondary)
dc.titleCharacteristic varieties of arrangements
dc.typetext

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