Nef cones of some Quot schemes on a Smooth Projective Curve

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

On Projective Varieties with Nef Anticanonical Divisors

The aim of this note is to prove a structure theorem for projective varieties with nef anticanonical divisors (the Main Theorem). In [18], we showed that if X is smooth and −KX is nef, then the Albanese map AlbX : X → Alb(X) is surjective and has connected fibers (i.e., it is a fiberspace map). In this note we apply the techniques which have been developed in [2],[14] and [19] to prove the foll...

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...