On the Taub-NUT type hyper-Kähler metrics on the Hilbert schemes of n points on C2

Research output: Contribution to journalArticle

Abstract

We study some kind of deformations of hyper-Kähler quotients including toric hyper-Kähler manifolds and quiver varieties. It is well-known that Taub-NUT deformations are defined for toric hyper-Kähler manifolds, and the similar deformations were introduced for ALE hyper-Kähler manifolds of type Dk by Dancer, using the complete hyper-Kähler metric on the cotangent bundle of complexification of compact Lie group. It is generalized to more general hyper-Kähler quotients by Dancer and Swann, and such deformations are called hyper-Kähler modifications. In this article we generalize their deformations and apply them to the Hilbert schemes of n points on C2.

Original languageEnglish
Pages (from-to)76-96
Number of pages21
JournalDifferential Geometry and its Application
Volume53
DOIs
Publication statusPublished - 2017 Aug 1

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Hilbert Scheme
Metric
Quotient
Lie groups
Complexification
Cotangent Bundle
Quiver
Compact Lie Group
Generalise

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

On the Taub-NUT type hyper-Kähler metrics on the Hilbert schemes of n points on C2 . / Hattori, Kota.

In: Differential Geometry and its Application, Vol. 53, 01.08.2017, p. 76-96.

Research output: Contribution to journalArticle

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