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

Kota Hattori

doi:10.1016/j.difgeo.2017.04.008

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

Kota Hattori

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 D_k 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 language	English
Pages (from-to)	76-96
Number of pages	21
Journal	Differential Geometry and its Application
Volume	53
DOIs	https://doi.org/10.1016/j.difgeo.2017.04.008
Publication status	Published - 2017 Aug 1

ASJC Scopus subject areas

Analysis
Geometry and Topology
Computational Theory and Mathematics

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10.1016/j.difgeo.2017.04.008

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title = "On the Taub-NUT type hyper-K{\"a}hler metrics on the Hilbert schemes of n points on C2",

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

author = "Kota Hattori",

note = "Funding Information: The author was supported by Grant-in-Aid for JSPS Fellows (23⋅1432) and Grant-in-Aid for Young Scientists (B) Grant Number 16K17598. The author was partially supported by JSPS Core-to-Core Program, “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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N2 - 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.

AB - 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.

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

Abstract

ASJC Scopus subject areas

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