Rational singularity

Summary

A rational singularity is a singular point that looks, from the point of view of sheaf cohomology, like a smooth point. It is defined by the vanishing of the higher direct images of the structure sheaf under a resolution. Quotient singularities, toric singularities and the ADE singularities are rational. Rational singularities play a central role in the minimal model program, since the log terminal singularities it uses are rational.