The Chow ring of punctual Hilbert schemes on toric surfaces

Author： Evain L.  

Publisher： Springer Publishing Company

ISSN： 1083-4362

Source： Transformation Groups, Vol.12, Iss.2, 2007-06, pp. : 227-249

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Abstract

Let X be a smooth projective toric surface, and the Hilbert scheme parametrizing the length d zero-dimensional subschemes of X. We compute the rational Chow ring . More precisely, if is the two-dimensional torus contained in X, we compute the rational equivariant Chow ring 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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