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Analytic sheaf

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A sheaf $ F $ on an analytic space $ X $ such that for any point $ x \in X $ the set $ F _ {x} $ is a module over the ring $ {\mathcal O} _ {x} $ of germs of holomorphic functions at the point $ x $, and such that the mapping $ (f , \alpha ) \rightarrow f \alpha $, defined on the set of pairs $ ( f, \alpha ) $ where $ f \in {\mathcal O} _ {x} $, $ \alpha \in F _ {x} $, is a continuous mapping of $ {\mathcal O} \times F $ into $ F $ for $ x \in X $.

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References

[a1] H. Grauert, R. Remmert, "Theory of Stein spaces" , Springer (1979) (Translated from German)
[a2] H. Grauert, R. Remmert, "Coherent analytic sheaves" , Springer (1984) (Translated from German)
How to Cite This Entry:
Analytic sheaf. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Analytic_sheaf&oldid=45181
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article