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The Chow ring of punctual Hilbert schemes of toric surfaces

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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Dates and versions

hal-00004600 , version 1 (29-03-2005)
hal-00004600 , version 2 (14-12-2005)

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Cite

Laurent Evain. The Chow ring of punctual Hilbert schemes of toric surfaces. 2005. ⟨hal-00004600v2⟩
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