# proper mapping theorem

###### Theorem.

Let $X$ and $Y$ be complex manifolds, $f\colon X\to Y$ be a proper (http://planetmath.org/ProperMap) holomorphic map, and $V\subset X$ be a complex analytic subvariety of $X.$ Then $f(V)$ is a subvariety of $Y.$

## References

• 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
Title proper mapping theorem ProperMappingTheorem 2013-03-22 17:41:01 2013-03-22 17:41:01 jirka (4157) jirka (4157) 4 jirka (4157) Theorem msc 32A60 msc 32A25