# 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 AnalyticSheaf 2013-03-22 17:39:02 2013-03-22 17:39:02 jirka (4157) jirka (4157) 5 jirka (4157) Definition msc 32C35