The Chow ring of punctual Hilbert schemes of toric surfaces

Details The Chow ring of punctual Hilbert schemes of toric surfaces The Chow ring of punctual Hilbert schemes of toric surfaces

2005-03-30

arxiv.org/abs/math/0503697v2

Mathematics

Algebraic Geometry

27 pages, updated version, minor modifications

Scientific paper

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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