The Chow ring of punctual Hilbert schemes of toric surfaces

2005/03/30 by Laurent Evain, Evain, Laurent
Mathematics · #14C05 #14C15 #14L30 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0503697

openalex publication_date 2005/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective toric surface, and H^d(X) the Hilbert scheme parametrising the length d zero-dimensional subschemes of X. We compute the rational Chow ring A^*(H^d(X))_Q. More precisely, if T is the two-dimensional torus contained in X, we compute the rational equivariant Chow ring A_T^*(H^d(X))_Q and the usual Chow ring is an explicit quotient of the equivariant Chow ring. The case of some quasi-projective toric surfaces such as the affine plane are described by our method too.

Citations

• Hilbert schemes, Hecke algebras and the Calogero-Sutherland system

Related

• Intersection theory on punctual Hilbert schemes and graded Hilbert schemes
• On the equivariant cohomology of Hilbert schemes of points in the plane
• The Chow Ring of the Hilbert Scheme of Rational Normal Curves
• Equations for Chow and Hilbert Quotients
• Irreducible components of the equivariant punctual Hilbert schemes