# nLab normal variety

An algebraic variety or an algebraic scheme $X$ is normal if at every point $p$ the stalk ${𝒪}_{X,x}$ is an integrally closed domain?. For every variety $X$ there is a morphism $X\to 𝒳$ which is universal among all morphisms from $X$ into normal varieties; $𝒳$ (or more precisely $𝒳$ together with the universal morphism) is said to be the normalization of $X$.

Revised on March 6, 2013 19:24:34 by Zoran Škoda (161.53.130.104)