Properties of the residual circle action on a toric hyperkahler variety

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dc.creatorHarada, Megumi
dc.creatorProudfoot, Nicholas J.
dc.date2002-07-01
dc.date2004-01-19
dc.date.accessioned2026-07-07T04:49:28Z
dc.date.available2026-07-07T04:49:28Z
dc.descriptionWe consider a manifold X obtained by a Kahler reduction of C^n, and we define its hyperkahler analogue M as a hyperkahler reduction of T^*C^n = H^n by the same group. In the case where the group is abelian and X is a smooth toric variety, M is a toric hyperkahler manifold, as defined by Bielawski-Dancer, and further studied by Konno and Hausel-Sturmfels. The manifold M carries a natural action of S^1, induced by the scalar action of S^1 on the fibers of T^*C^n. In this paper we study this action, computing its fixed points and its equivariant cohomology. As an application, we use the associated Z/2 action on the real locus of M to compute a deformation of the Orlik-Solomon algebra of a smooth, generic, real hyperplane arrangement, depending nontrivially on the affine structure of the arrangement. This deformation is given by the Z/2-equivariant cohomology of the complement of the complexification, where Z/2 acts by complex conjugation.
dc.description21 pages, 5 figures. Minor errors in Section 1 corrected
dc.identifierhttps://arxiv.org/abs/math/0207012
dc.identifierhttp://arxiv.org/abs/math/0207012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64439
dc.subjectDifferential Geometry
dc.subjectCombinatorics
dc.subjectSymplectic Geometry
dc.subject53C26; 52C35
dc.titleProperties of the residual circle action on a toric hyperkahler variety
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