# nLab normal variety

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

Last revised on March 6, 2013 at 19:24:34. See the history of this page for a list of all contributions to it.