Geometry of rational double points

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One of the most important classes of normal surface singularities are rational double points. Their deformations and resolutions over the complex numbers have been are now very well understood thanks to work of Brieskorn, Grothendieck, Slodowy, and Springer, who connected them to the theory of linear algebraic groups. However, over fields of positive characteristic, and especially if the characteristic is bad in the sense of Slodowy, the situation is still quite unclear. The goal of this project is to clarify this.