The hypertoric intersection cohomology ring

TL;DR

This paper computes the equivariant intersection cohomology ring of hypertoric varieties functorially, establishing a natural ring structure, especially in the unimodular case, using localization techniques in equivariant derived categories.

Contribution

It provides a functorial method to compute the intersection cohomology ring of hypertoric varieties and links the ring structure to sheaf-theoretic constructions in the equivariant derived category.

Findings

Ring structure induced by sheaves in the unimodular case

Localization functor maps equivariant sheaves to sheaves on a poset

Explicit computation of the intersection cohomology ring

Abstract

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.