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Transactions of the American Mathematical Society

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

 

 

Characterization of privileged polydomains


Author: Yum Tong Siu
Journal: Trans. Amer. Math. Soc. 193 (1974), 329-357
MSC: Primary 32C35; Secondary 46E15
DOI: https://doi.org/10.1090/S0002-9947-1974-0355100-0
MathSciNet review: 0355100
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Abstract: This paper gives a number of equivalent conditions for a bounded polydomain to be privileged with respect to a coherent analytic sheaf in the sense of Douady. One of the equivalent conditions is in terms of the homological codimensions of the sheaf at the boundary of the polydomain. In the case of a polydisc, this condition about homological codimensions coincides with a conjecture of Douady. The other equivalent conditions concern some weaker concepts of privilegedness and the existence of privileged sets at the boundary.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0355100-0
Keywords: Coherent analytic sheaves, homological codimensions, privileged sets, Banach spaces
Article copyright: © Copyright 1974 American Mathematical Society