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.
ASJC Scopus subject areas
- Geometry and Topology
- Computational Theory and Mathematics