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 Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 838–850 (Mi izv990)

Criteria for holomorphic completeness

V. D. Golovin

Abstract: It is proved that a complex space which is countable at infinity is holomorphically complete if and only if the homology groups with compact supports for coherent analytic sheaves are trivial in the nonzero dimensions and the topological vector space of zero-dimensional homology with compact support of the structure sheaf is separated (Hausdorff). This result is then applied to complex spaces which can be represented as a union of an increasing sequence of holomorphically complete open sets and to complex spaces which locally admit holomorphically complete mappings into holomorphically complete spaces.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:1, 817–827

Bibliographic databases:

UDC: 515.17
MSC: 32C15, 32C35

Citation: V. D. Golovin, “Criteria for holomorphic completeness”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 838–850; Math. USSR-Izv., 39:1 (1992), 817–827

Citation in format AMSBIB
\Bibitem{Gol91} \by V.~D.~Golovin \paper Criteria for holomorphic completeness \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1991 \vol 55 \issue 4 \pages 838--850 \mathnet{http://mi.mathnet.ru/izv990} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1137588} \zmath{https://zbmath.org/?q=an:0783.32007|0739.32012} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..39..817G} \transl \jour Math. USSR-Izv. \yr 1992 \vol 39 \issue 1 \pages 817--827 \crossref{https://doi.org/10.1070/IM1992v039n01ABEH002227} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JQ84600006} 

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This publication is cited in the following articles:
1. V. D. Golovin, “Criteria for holomorphic completeness. II”, Izv. Math., 59:4 (1995), 671–676
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