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Les groupes de Chow de Hilb\(^ 4{\mathbb{P}}^ 2\) et une base pour \(A^ 2,A^ 3,A^{2d-2},A^{2d-3}\) de Hilb\(^ d{\mathbb{P}}^ 2\). (The Chow groups of Hilb\(^ 4{\mathbb{P}}^ 2\) and a base of \(A^ 2,A^ 3,A^{2d- 2},A^{2d-3}\) of Hilb\(^ d{\mathbb{P}}^ 2)\). (French) Zbl 0606.14004

The main result in this paper is a description of an additive basis for the Chow groups \(A^ i(Hilb^ d({\mathbb{P}}^ 2))\) for \(d\leq 4\) and all i, and for all d and \(i=2, 3, 2d-3, 2d-2.\) Since the writing of this paper, the author, in a joint work with I. Sols [”A base of the homology groups of the Hilbert scheme of points in the plane” (preprint, Madrid 1987)] has generalised the result to cover all cases of d and i. The basis is given as the rational equivalence classes of geometrically constructed subvarieties of the Hilbert scheme. The importance of the result comes from the fact that in each of these basic subvarieties, the general point corresponds to a configuration of d distinct points of the plane. This makes the basis well suited for attacking enumerative problems.
Reviewer: S.A.Strømme

MSC:

14C15 (Equivariant) Chow groups and rings; motives
14C05 Parametrization (Chow and Hilbert schemes)
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