Integral cohomology of Hilbert schemes of points on surfaces
type: Item
instance of: scholarly article
title: Integral cohomology of Hilbert schemes of points on surfaces
zbMATH Open document ID: 1166.14015
author: Wei-Ping Li
author: Zhenbo Qin
published in: Communications in Analysis and Geometry
publication date: 2009-04-14T00:00:00Z
review text: The purpose of this paper is to settle a conjecture raised by \textit{Z. Qin} and \textit{W. Wang} in their paper ``Integral operators and integral cohomology classes of Hilbert schemes'' [Math. Ann. 331, No. 3, 669--692 (2005; Zbl 1081.14006)]. The conjecture states that, under a particular hypothesis, certain homological operators are integral. To this end the authors use topological \(K\)-theory and the algebra of rings of symmetric functions. The result is then used to obtain explicit generators for the integral cohomology of the Hilbert scheme of \(n\) points on a smooth projective surface which has no odd cohomology. The paper is well written, thorough and contains the necessary information on Hilbert schemes of points on surfaces. Several computations are worked out explicitly.
reviewed by: Morgan Sherman
Mathematics Subject Classification ID: 14F99
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 5543231
zbMATH Keywords: Hilbert schemes
zbMATH Keywords: integral cohomology
MaRDI profile type: Publication
full work available at URL: cag.2008.v16.n5.a3
OpenAlex ID: W2000766289
DOI: 10.4310/CAG.2008.V16.N5.A3
description: scientific article; zbMATH DE number 5543231