Resolution of simple singularities

In this chapter, we shall construct minimal resolutions of simple singularities using Hilbert schemes of points on C. These resolutions inherit the hyper-Kahler structures from those on Hilbert schemes. This construction will give us a new interpretation Kronheimer s construction of ALE spaces [49] in terms of Hilbert schemes. 

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Remark 4.3. The hyper-Kahler structures on the minimal resolutions of simple singularities were constructed by Kronheimer [49]. His construction will be explained later. 

Gauge theory on resolution of simple singularities and simple Lie algebras. Inter. Math. Res. 

We shall see that (C ) and the minimal resolution of the simple singularities has decomposable diagonal class in Ghapter 4. 

Conversely, starting from this description, Kronheimer constructed resolutions of the simple singularities [49] as follows. In order to explain the hyper-Kahler structures, we use the description given in Theorem 2.1 rather than that in Theorem 1.14. Let M = Hom(l/, Q 0 F) Hom(VF, V) Hom(F, W). Then its F-hxed point is... 

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