# proper mapping theorem

###### Theorem.

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

## References

- 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.

Title | proper mapping theorem |
---|---|

Canonical name | ProperMappingTheorem |

Date of creation | 2013-03-22 17:41:01 |

Last modified on | 2013-03-22 17:41:01 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 4 |

Author | jirka (4157) |

Entry type | Theorem |

Classification | msc 32A60 |

Classification | msc 32A25 |