On Ellingsrud and Strømme's cell decomposition of \(\mathbf{Hilb}^n_{\mathbb{A}^2_\mathbb{C}}\)
\textit{G. Ellingsrud} and \textit{S.A. Strømme} [Invent. Math. 91, 365--370 (1988; Zbl 1064.14500)] constructed a cell decomposition of the Hilbert scheme \(\text{Hilb}^d(\mathbb{P}^2)\) induced by the natural torus action. Unfortunately, the constructed families there were not always finite over their base, as the author points out in an example, using Gröbner basis computations. Therefore, some auxiliary lemmas in [loc. cit.] are incorrect (though the main results hold true) . The author recovers the main results of [loc. cit.] by a modification of the constructed families. Namely, it is shown that after restriction to the preimages the families over the cells have the desired properties.
scientific article; zbMATH DE number 2156042
scientific article