Normal scheme

In algebraic geometry, an algebraic variety or schemeX is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine varietyX (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. A variety X over a field is normal if and only if every finitebirational morphism from any variety Y to X is an isomorphism.

Normal varieties were introduced by Zariski.