---- > [!definition] Definition. ([[normal scheme]]) > A [[scheme]] $X$ is **normal** if all its [[(pre)sheaf stalk|stalks]] are [[integral closure|integrally closed]] [[integral domain|domains]][^1] as [[local ring|(local)]] [[ring|rings]]. ^definition ---- #### [^1]: Recall that the [[integral closure]] of an [[integral domain]] $A$ is by default taken with respect to its [[field of fractions]] $\text{Frac }A$. ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```