Numerical characterization of complex torus quotients

Orbifold Cohomology of Torus Quotients

We introduce the inertial cohomology ring NH T (Y) of a stably almost complex manifold carrying an action of a torus T . We show that in the case that Y has a locally free action by T , the inertial cohomology ring is isomorphic to the Chen-Ruan orbifold cohomology ring H∗CR(Y/T ) (as defined in [Chen-Ruan]) of the quotient orbifold Y/T . For Y a compact Hamiltonian T -space, we extend to orbif...

Good Quotients of Torus Actionsj

Torus actions on compact quotients

For a reductive Lie group G and a uniform lattice Γ in G we consider the compact space Γ\G. We fix a maximal torus H in G and consider its action on the compact quotient Γ\G. Assuming H to be noncompact we will prove a Lefschetz formula relating compact orbits as local data to the action of the torus H on a global cohomology theory (tangential cohomology). The compact orbits are parametrized mo...

Torus quotients as global quotients by finite groups

This article is motivated by the following local-to-global question: is every variety with tame quotient singularities globally the quotient of a smooth variety by a finite group? We show that this question has a positive answer for all quasi-projective varieties which are expressible as a quotient of a smooth variety by a split torus (e.g. simplicial toric varieties). Although simplicial toric...

Complete Invariants for Hamiltonian Torus Actions with Two Dimensional Quotients

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.