##  [Nonnormal Variety](/nonnormal-variety) 

  ##  [Nonnormal Variety](https://algebra.quantumdictionary.io/nonnormal-variety-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A variety or scheme that is not normal, i.e., at some point one of its local rings is not integrally closed in its total ring of fractions. Nonnormality produces branch-like phenomena, failure of integral closure, and can manifest as cusps, pinch points, or more subtle failures of being integrally closed in codimension one.