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The Equivariant Chow rings of quot schemes

Tom Braden·Linda Chen·Frank Sottile
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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.

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Tom Braden, Linda Chen, Frank Sottile. 2006-02-08. The Equivariant Chow rings of quot schemes. https://arxiv.org/abs/math/0602161

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