Simple surface singularities

Journal article, 2017

By the famous ADE classification, rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities whose resolution graph can be obtained from the graph of a rational double point or rational triple point by making any number of vertex weights more negative. We show that no other rational singularities can be simple. We prove simpleness only for special classes of singularities, namely rational quadruple points or sandwiched singularities.