Hilbert series of symplectic quotients by the 2-torus

Symplectic quotients by a nonabelian group and by its maximal torus

This paper examines the relationship between the symplectic quotientX//G of a Hamiltonian G-manifold X , and the associated symplectic quotient X//T , where T ⊂ G is a maximal torus, in the case in which X//G is a compact manifold or orbifold. The three main results are: a formula expressing the rational cohomology ring of X//G in terms of the rational cohomology ring of X//T ; an ‘integration’...

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...

The Hilbert Series of a Linear Symplectic Circle Quotient

We study the Hilbert series of the graded algebra of regular functions on a symplectic quotient of a unitary circle representation and elaborate explicit formulas for the lowest coefficients of the Laurent expansion of such a Hilbert series in terms of rational symmetric functions of the weights. Considerable efforts are devoted to including the cases where the weights are degenerate. We find t...

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