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Izvestiya: Mathematics, 1995, Volume 59, Issue 4, Pages 671–676
DOI: https://doi.org/10.1070/IM1995v059n04ABEH000029
(Mi im29)
 

Criteria for holomorphic completeness. II

V. D. Golovin
References:
Abstract: It is proved that a complex space $X$ of finite dimension $d$ is holomorphically complete if and only if the following conditions hold:
1) for an arbitrary point $x_0\in X$ there exists analysis sets $M_n\subset\dots\subset M_1\subset M_0=X$ and holomorphic function $f_i\in\Gamma(M_{i-1};\mathscr O_{M_{i-1}})$, $i=1,\dots,n$, such that $M_i=\{x\in M_{i-1}:f_i(x)=0\}$, and $\mathscr O_{M_i}=\mathscr O_{M_{i-1}}/f_i\mathscr O_{M_{i-1}}\mid M_i$ for each $i=1,\dots,n$, and $x_0$ is an isolated point in $M_n$;
2) $H^k(X;\mathscr O_X)=0$, for $k=1,\dots,d-1$.
Received: 08.04.1993
Bibliographic databases:
MSC: 32C99
Language: English
Original paper language: Russian
Citation: V. D. Golovin, “Criteria for holomorphic completeness. II”, Izv. Math., 59:4 (1995), 671–676
Citation in format AMSBIB
\Bibitem{Gol95}
\by V.~D.~Golovin
\paper Criteria for holomorphic completeness.~II
\jour Izv. Math.
\yr 1995
\vol 59
\issue 4
\pages 671--676
\mathnet{http://mi.mathnet.ru//eng/im29}
\crossref{https://doi.org/10.1070/IM1995v059n04ABEH000029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1356348}
\zmath{https://zbmath.org/?q=an:0871.32004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000169556400002}
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