Rational Singularity - Formulations

Formulations

Alternately, one can say that has rational singularities if and only if the natural map in the derived category

is a quasi-isomorphism. Notice that this includes the statement that and hence the assumption that is normal.

There are related notions in positive and mixed characteristic of

• pseudo-rational

and

• F-rational

Rational singularities are in particular Cohen-Macaulay, normal and Du Bois. They need not be Gorenstein or even Q-Gorenstein.

Log terminal singularities are rational.