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.

单词	AnalyticSheaf
释义	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.
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