##  [Projective Variety](/projective-variety) 

  ##  [Projective Variety](https://puremath.quantumdictionary.io/projective-variety-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A projective variety is a subset X of projective space P^n over a field (typically algebraically closed) defined as the common zero locus of a collection of homogeneous polynomials; it is endowed with the Zariski topology and schemes or coordinate ring structures refine its algebraic structure.