On Ellingsrud and Strømme's cell decomposition of \(\mathbf{Hilb}^n_{\mathbb{A}^2_\mathbb{C}}\)
type: Item
instance of: scholarly article
title: On Ellingsrud and Strømme's cell decomposition of \(\mathbf{Hilb}^n_{\mathbb{A}^2_\mathbb{C}}\)
zbMATH Open document ID: 1064.14005
published in: Inventiones Mathematicae
publication date: 2005-04-14T00:00:00Z
review text: \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.
reviewed by: Olaf Teschke
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14C15
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 2156042
author: Mark Huibregtse
MaRDI profile type: Publication
full work available at URL: s00222-004-0409-9
OpenAlex ID: W1970448766
cites work: Introduction to Grothendieck duality theory
cites work: Some theorems on actions of algebraic groups
cites work: On a cell decomposition of the Hilbert scheme of points in the plane.
cites work: Algebraic Families on an Algebraic Surface
cites work: Q3322387
cites work: \(t,q\)-Catalan numbers and the Hilbert scheme.
DOI: 10.1007/S00222-004-0409-9
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description: scientific article; zbMATH DE number 2156042