Geometry of rational double points

法向曲面奇点中最重要的一类是有理双点。由于Brieskorn、Grothendieck、Slodowy和Springer的工作，他们在复数上的变形和分解现在已经被很好地理解了，他们将它们与线性代数群理论联系起来。然而，对于正特征的领域，特别是如果特征在懒惰意义上是坏的，情况仍然相当不清楚。这个项目的目标就是澄清这一点。

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.