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One dimensional fibering over q-complete spaces

Published online by Cambridge University Press:  22 January 2016

Viorel Vâjâitu
Viorel Vâjâitu*
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O.Box 1-764, RO-70700 Bucharest, Romania, [email protected]
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Abstract.

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We show that if E → X is a locally trivial holomorphic fibrations whose fiber is an open Riemann surface and X is a q-complete space, then E is q-complete.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 99 - 106
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Andreotti, A. and Grauert, H., Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193–259.Google Scholar
[2] Ballico, E., Coverings of complex spaces and q-completeness, Riv. Mat. Univ. Parma (4), 7 (1981), 443–452.Google Scholar
[3] Docquier, F. and Grauert, H., Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann., 140 (1960), 94–123.Google Scholar
[4] Jennane, B., Groupes de cohomologie d’un fibre holomorphe a base et a fibre de Stein, Invent. Math., 54 (1979), 75–79.Google Scholar
[5] Mok, N., The Serre problem on Riemann surfaces, Math. Ann., 258 (1981), 145–168.Google Scholar
[6] Peternell, M., Algebraische Varietäten und q-vollständige komplexe Räume, Math. Z., 200 (1989), 547–581.Google Scholar
[7] Serre, J. P., Quelques problèmes globaux relatifs aux variétés de Stein, Colloque sur les fonctions de plusieurs varibales, Bruxelles 1953, 53–68.Google Scholar
[8] Siu, Y.-T., Pseudoconvexity and the problem of Levi, Bull. Amer. Math. Soc., 84 (1978), 481–511.Google Scholar
[9] Skoda, H., Fibrés holomorphes à base et à fibre de Stein, Invent. Math., 43 (1977), 97–107.Google Scholar
[10] Stehlé, J.-L., Fonctions plurisousharmoniques et convexité holomorphe de certain fibrés analytiques, Lecture Notes, 474, Séminaire P. Lelong, 1973/74, 155–180.Google Scholar
[11] Vâjâitu, V., Approximation theorems and homology of q-Runge domains in complex spaces, J. reine angew. Math., 449 (1994), 179–199.Google Scholar
[12] Vâjâitu, V., Cohomology groups of locally q-complete morphisms with p-complete base, Math. Scandinavica, 79 (1996), 161–175.Google Scholar