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** $X$.

category: algebraic geometry

Last revised on January 29, 2021 at 04:06:21. See the history of this page for a list of all contributions to it.