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The Chow ring of punctual Hilbert schemes of toric surfaces

Laurent Evain
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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.

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Laurent Evain. 2005-12-15. The Chow ring of punctual Hilbert schemes of toric surfaces. https://arxiv.org/abs/math/0503697

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