ADE singularity

Summary

The ADE singularities, also called Du Val singularities, simple surface singularities or rational double points, are the simplest singular points of complex surfaces. They are the quotients $\C^2/G$ by finite subgroups $G$ of the special linear group $SL(2, \C)$. They come in two infinite families $A_n$ and $D_n$ and three exceptional cases $E_6$, $E_7$, $E_8$, matching the simply laced Dynkin diagrams. The match is visible in the minimal resolution, whose exceptional curves meet in the pattern of the Dynkin diagram.