The Equivariant Chow Rings Of Quot Schemes

Authors

T. Braden
Linda Chen, Swarthmore CollegeFollow
F. Sottile

Document Type

Article

Publication Date

12-1-2008

Published In

Pacific Journal Of Mathematics

Abstract

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 the geometry of families of torus-invariant curves. As part of this calculation, we give a complete description of the torus-invariant curves on the quot scheme and show that each family is a product of projective spaces.

Comments

This work is freely available courtesy of the Mathematical Sciences Publishers.

Recommended Citation

T. Braden, Linda Chen, and F. Sottile. (2008). "The Equivariant Chow Rings Of Quot Schemes". Pacific Journal Of Mathematics. Volume 238, Issue 2. 201-232. DOI: 10.2140/pjm.2008.238.201
https://works.swarthmore.edu/fac-math-stat/51