PlanetMath: proper mapping theorem

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proper mapping theorem

(Theorem)

Theorem 1 Let $X$ and $Y$ be complex manifolds, $f \colon X \to Y$ be a proper holomorphic map, and $V \subset X$ be a complex analytic subvariety of $X.$ Then $f(V)$ is a subvariety of $Y.$

Bibliography

1: Hassler Whitney. Complex Analytic Varieties. Addison-Wesley, Philippines, 1972.

"proper mapping theorem" is owned by jirka.

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Cross-references: subvariety, complex analytic subvariety, map, holomorphic, complex manifolds

This is version 1 of proper mapping theorem, born on 2007-12-12.
Object id is 10123, canonical name is ProperMappingTheorem.
Accessed 658 times total.

Classification:

AMS MSC:	32A60 (Several complex variables and analytic spaces :: Holomorphic functions of several complex variables :: Zero sets of holomorphic functions)
	32A25 (Several complex variables and analytic spaces :: Holomorphic functions of several complex variables :: Integral representations; canonical kernels )

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