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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Contributor : Laurent Evain <>
Submitted on : Wednesday, December 14, 2005 - 6:59:19 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM
Document(s) archivé(s) le : Monday, September 20, 2010 - 1:19:26 PM

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

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