GKM theory for orbifold stratified spaces and application to singular toric varieties

TL;DR

This paper extends GKM theory to orbifold stratified spaces and introduces new classes of polytopes and toric varieties, enabling computation of their equivariant cohomology.

Contribution

It develops GKM theory for orbifold stratified spaces and introduces almost simple polytopes and divisive toric varieties, broadening the scope of equivariant cohomology computations.

Findings

GKM theory applied to orbifold stratified spaces

Introduction of almost simple polytopes and divisive toric varieties

Computation of equivariant cohomology for new classes of toric varieties

Abstract

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce the notion of an \emph{almost simple polytope}, as well as a \emph{divisive toric variety} generalizing the concept of a divisive weighted projective space. We employ the GKM theory to compute the generalized equivariant cohomology theories of toric varieties associated to almost simple polytopes and divisive toric varieties.