A subvariety of an algebraic variety that is not the entire variety. The proper subvarieties of a line are its nonempty finite subsets, the proper subvarieties of a plane are its nonempty finite subsets, the unions of finitely many of its lines and, more in general, of finitely many algebraic curves contained in it.

# Proper Subvariety

## See also

Algebraic Variety, Variety
*This entry contributed by Margherita
Barile*

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## Cite this as:

Barile, Margherita. "Proper Subvariety." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/ProperSubvariety.html