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On the quasi-asymptotically locally Euclidean geometry of Nakajima's metric

Part of: Singularities Global differential geometry

Published online by Cambridge University Press:  29 June 2010

Gilles Carron
Gilles Carron
Affiliation:
Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France (gilles.carron@math.univ-nantes.fr)
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Abstract

We show that on the Hilbert scheme of n points on ℂ2, the hyperkähler metric constructed by Nakajima via hyperkähler reduction is the quasi-asymptotically locally Euclidean (QALE) metric constructed by Joyce.

Keywords

hyperkähler manifoldQALE metrichyperkähler reduction

MSC classification

Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C26: Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 32S20: Global theory of singularities; cohomological properties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 1 , January 2011 , pp. 119 - 147
Copyright
Copyright © Cambridge University Press 2010

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