# analytic sheaf

Let $M$ be a complex manifold^{}. Let $\mathcal{O}$ be the sheaf of germs of analytic functions^{} (which is a sheaf of rings) and let $\mathcal{F}$ be a sheaf of $\mathcal{O}$-modules. $\mathcal{F}$ is then called an *analytic sheaf*.

###### Example.

Suppose $X$ is an analytic vector bundle over $M$. Then the sheaf of germs of analytic sections of $X$ is an analytic sheaf.

###### Example.

The sheaf of germs of meromorphic functions on $M$ is an analytic sheaf.

## References

- 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.

Title | analytic sheaf |
---|---|

Canonical name | AnalyticSheaf |

Date of creation | 2013-03-22 17:39:02 |

Last modified on | 2013-03-22 17:39:02 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Definition |

Classification | msc 32C35 |