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Bases for the homology groups of the Hilbert scheme of points in the plane. (English) Zbl 0728.14001

G. Ellingsrud and S. A. Strømme [Invent. Math. 91, No.2, 365-370 (1988; Zbl 0654.14003)] have found a cell decomposition for the space \(Hilb^ d(P^ 2)\), the Hilbert scheme of length \(d\) subschemes of \({\mathbb{P}}^ 2\). This implies that the Chow group \(A_*(Hilb^ d(P^ 2))\) is a free abelian group. However, the general element in a cell of this decomposition will correspond to a nonreduced scheme in \({\mathbb{P}}^ 2.\)
The authors give a new basis for the Chow group which avoids the difficulty above. In the case \(d=3\), this is essentially the basis given by G. Elencwajg and P. Le Barz in an earlier paper [see e.g. C. R. Acad. Sci., Paris, Sér. I 301, 635-638 (1985; Zbl 0597.14005)].
Reviewer: L.Ein (Chicago)

MSC:

14C05 Parametrization (Chow and Hilbert schemes)
14F45 Topological properties in algebraic geometry
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References:

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