The Equivariant Chow rings of quot schemes
Algebraic Geometry
2010-03-29 v2
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.
Keywords
Cite
@article{arxiv.math/0602161,
title = {The Equivariant Chow rings of quot schemes},
author = {Tom Braden and Linda Chen and Frank Sottile},
journal= {arXiv preprint arXiv:math/0602161},
year = {2010}
}
Comments
Revised slightly. Clarifed some statements and remove one straightforward proof. 26 pages, many .eps figures