Quot Schemes for Kleinian Orbifolds

Two-generator Kleinian orbifolds

We give a complete list of orbifolds uniformised by discrete nonelementary two-generator subgroups of PSL(2, C) without invariant plane whose generators and their commutator have real traces. Mathematics Subject Classification (2000): Primary: 57M12; Secondary: 30F40, 22E40, 57M50.

On Punctual Quot Schemes for Algebraic Surfaces

Let S be a smooth projective surface over the field of complex numbers C. Fix a closed point s ∈ S and a pair of positive integers r, d. By results of Grothendieck (cf. [6], [11]) there exists a projective scheme Quot [s] (r, d) parametrizing all quotient sheaves O ⊕r S → A of length d supported at s. We consider this scheme with its reduced scheme structure and call it the punctual Quot scheme...

Stable maps and Quot schemes

0 Stable maps and 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...