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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Holomorphic convexity of compact sets in analytic spaces and the structure of algebras of holomorphic germs

Author: William R. Zame
Journal: Trans. Amer. Math. Soc. 222 (1976), 107-127
MSC: Primary 32E25; Secondary 32C35
MathSciNet review: 0425179
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Abstract: Let $(X,{\mathcal {O}_X})$ be a reduced analytic space and let K be a compact, holomorphically convex subset of X. It is shown that analogs of Cartan’s Theorems A and B are valid for coherent analytic sheaves on K. This result is applied to the study of the algebra of germs on K of functions holomorphic near K. In particular, characterizations of finitely generated ideals, prime ideals and homomorphisms are obtained.

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Keywords: Holomorphic convexity, holomorphic germs, analytic spaces, Theorem B
Article copyright: © Copyright 1976 American Mathematical Society