nLab normal variety

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Idea

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

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