Characterization of privileged polydomains

Siu, Yum Tong

doi:10.1090/S0002-9947-1974-0355100-0

Characterization of privileged polydomains
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Trans. Amer. Math. Soc. 193 (1974), 329-357 Request permission

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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