The equivariant Chow rings of quot schemes

The Equivariant Chow Rings Of Quot Schemes

We give a presentation for the (integral) torus-equivariant Chow ring of the quot scheme, a smooth compactification of the space of rational curves of degree d in the Grassmannian. For this presentation, we refine Evain’s extension of the method of Goresky, Kottwitz, and MacPherson to express the torus-equivariant Chow ring in terms of the torus-fixed points and explicit relations coming from t...

Stable maps and Quot schemes

Equivariant Chow cohomology of toric varieties

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization holds in equivariant Chow cohomology with integer coefficients. We also compute the equivariant Chow cohomology of toric prevarieties and general complex hyper...

Equivariant Chow Cohomology of Nonsimplicial Toric Varieties

Abstract. For a toric variety XΣ determined by a polyhedral fan Σ ⊆ N , Payne shows that the equivariant Chow cohomology is the Sym(N)–algebra C(Σ) of integral piecewise polynomial functions on Σ. We use the CartanEilenberg spectral sequence to analyze the associated reflexive sheaf C(Σ) on PQ(N), showing that the Chern classes depend on subtle geometry of Σ and giving criteria for the splittin...

0 Stable maps and Quot schemes