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Determination of the Chow ring of \(\text{Hilb}^ 3\mathbb P^ 2\). (Détermination de l’anneau de Chow de \(\text{Hilb}^ 3\mathbb P^ 2\).) (French) Zbl 0597.14005
A description of the Chow ring of the Hilbert scheme \(\text{Hilb}^ 3({\mathbb P}^ 2)\) is given. The additive structure of this ring was determined by A. Hirschowitz [C. R. Acad. Sci., Paris, Sér. I 298, 87–89 (1984; Zbl 0563.14001)]. The authors construct geometrically a set of cycles and compute the degrees of their zero-dimensional intersections. From these numbers and the knowledge of the Betti numbers, they conclude that the given set of cycles is an additive basis.
Reviewer: S. A. Strømme

14C05 Parametrization (Chow and Hilbert schemes)
14C15 (Equivariant) Chow groups and rings; motives
Zbl 0563.14001