The Chow ring of punctual Hilbert schemes of toric surfaces

Laurent Evain (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: cohomology; Hilbert scheme; toric; Chow ring; equivariant

Domaines: Géométrie algébrique [math.AG]

Laurent Evain. The Chow ring of punctual Hilbert schemes of toric surfaces. 2005. ⟨hal-00004600v1⟩