On the homology of the Hilbert scheme of points in the plane
type: Item
instance of: scholarly article
title: On the homology of the Hilbert scheme of points in the plane
zbMATH Open document ID: 0625.14002
DOI: 10.1007/BF01389419
author: Geir Ellingsrud
author: Stein Arild Strømme
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143422
review text: The authors calculate the Betti numbers of the Hilbert scheme of points in the plane. Observe that the maximal torus of SL(3) acts on \(Hilb^ d({\mathbb{P}}^ 2)\) with isolated fixed points. It follows from a result of Birula-Białynicki that \(Hilb^ d({\mathbb{P}}^ 2)\) has a cellular decomposition. Then the calculation of the Betti numbers reduces to a careful study of the representation of the torus at the tangent spaces of the fixed points. As a by-product to their method, the authors also obtain similar results about the punctual Hilbert scheme and the Hilbert scheme of points in the affine plane.
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4014872
zbMATH Keywords: Betti numbers of the Hilbert scheme of points in the plane
zbMATH Keywords: punctual Hilbert scheme
reviewed by: Lawrence Ein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4014872