In mathematics, more particularly in the field of algebraic geometry, a scheme
has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map from a regular scheme
For surfaces, rational singularities were defined by (Artin 1966).
has rational singularities if and only if the natural map in the derived category is a quasi-isomorphism.
There are related notions in positive and mixed characteristic of and Rational singularities are in particular Cohen-Macaulay, normal and Du Bois.