Hyperkahler analogues of Kahler quotients

Let X be a Kahler manifold that is presented as a Kahler quotient of C^n by nthe linear action of a compact group G. We define the hyperkahler analogue M of nX as a hyperkahler quotient of the cotangent bundle T^*C^n by the induced nG-action. Special instances of this construction include hypertoric varieties nand quiver varieties. Our aim is to provide a unified trea..