The equivariant Chow rings of quot schemes

Tom Braden, Linda Chen and Frank Sottile

Vol. 238 (2008), No. 2, 201–232

DOI: 10.2140/pjm.2008.238.201

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

equivariant cohomology, Chow ring, quot scheme, Grassmannian

Mathematical Subject Classification 2000

Primary: 55N91, 14M15, 14F43, 14C05

Milestones

Received: 28 November 2007

Revised: 14 July 2008

Accepted: 30 July 2008

Published: 1 December 2008