The hypertoric intersection cohomology ring

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we show that this ring structure is induced by a ring structure on the equivariant intersection cohomology sheaf in the equivariant derived category. The computation is given in terms of a localization functor which takes equivariant sheaves on a sufficiently nice stratified space to sheaves on a poset. T. Braden’s research was supported in part by NSF grant DMS-0201823. N. Proudfoot’s research was supported in part by an NSF Postdoctoral Research Fellowship and NSF grant DMS-0738335.