nLab normal variety

Idea

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 integral scheme $X$ there is a scheme $\mathcal{X}$ and a morphism $\mathcal{X} \to X$ which is universal among all dominant morphisms from normal schemes into $X$; $\mathcal{X}$ (together with the universal morphism) is said to be the normalization of $X$.

category: algebraic geometry