##  [Singular Point](/singular-point) 

  ##  [Singular Point](https://algebra.quantumdictionary.io/singular-point-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A point on an algebraic variety or scheme at which the local structure fails to be smooth or regular; equivalently, a point where the local ring is not regular or the Jacobian matrix of defining equations drops rank.