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