Implosion for hyperkahler manifolds

TL;DR

This paper introduces a hyperkahler analogue of symplectic implosion for SU(n) actions, constructing a stratified hyperkahler space via quiver diagrams and non-reductive GIT quotients, expanding hyperkahler geometry tools.

Contribution

It presents the first hyperkahler implosion construction for SU(n), linking quiver diagrams and non-reductive GIT to hyperkahler geometry.

Findings

Constructed a stratified hyperkahler space for SU(n) actions.

Provided a description via quiver diagrams.

Connected hyperkahler implosion with non-reductive GIT.

Abstract

We introduce an analogue in hyperkahler geometry of the symplectic implosion, in the case of SU(n) actions. Our space is a stratified hyperkahler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.