PlanetMath: analytic sheaf

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analytic sheaf

(Definition)

Let 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 1 Suppose is an analytic vector bundle over . Then the sheaf of germs of analytic sections of is an analytic sheaf.

Example 2 The sheaf of germs of meromorphic functions on is an analytic sheaf.

Bibliography

1: Lars Hörmander. An Introduction to Complex Analysis in Several Variables, North-Holland Publishing Company, New York, New York, 1973.
2: Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.

"analytic sheaf" is owned by jirka.

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Cross-references: functions, meromorphic, sections, vector bundle, rings, analytic functions, germs, sheaf, complex manifold
There are 2 references to this entry.

This is version 2 of analytic sheaf, born on 2007-12-02, modified 2007-12-03.
Object id is 10083, canonical name is AnalyicSheaf.
Accessed 172 times total.

Classification:

AMS MSC:

32C35 (Several complex variables and analytic spaces :: Analytic spaces :: Analytic sheaves and cohomology groups)

Pending Errata and Addenda

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