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On the Automorphism Group of a Holomorphic Fiber Bundle over A Complex Space

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Mathematical Institute, Nagoya University
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In [8], A. Morimoto proved that the automorphism group of a holomorphic principal fiber bundle over a compact complex manifold has a structure of a complex Lie group with the compact-open topology. The purpose of this paper is to get similar results on the automorphism groups of more general types of locally trivial fiber spaces over complex spaces. We study automorphisms of a holomorphic fiber bundle over a complex space which has a complex space Y as the fiber and a (not necessarily complex Lie) group G of holomorphic automorphisms of Y as the structure group (see Definition 3. l).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 91 - 106
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Fujimoto, H., Vector-valued holomorphic functions on a complex space, J. Math. Soc. Japan, 17 (1965), 52–66.CrossRefGoogle Scholar
[2] Hujimoto, F., On the holomorphic automorphism groups of complex spaces, Nagoya Math. J., 33 (1968), 85–106.CrossRefGoogle Scholar
[3] Grauert, H. and Remmert, R., Zur Theorie der Modifikationen. I, Math. Ann., 129 (1955), 274–296.Google Scholar
[4] Grauert, H. and Remmert, R., Komplexe Räume, Math. Ann., 136 (1958), 245–318.CrossRefGoogle Scholar
[5] Kaup, W., Infinitesimale Transformationsgruppen komplexer Räume, Math. Ann., 160 (1965), 72–92.CrossRefGoogle Scholar
[6] Kerner, H., Über die Fortsetzung holomorpher Abbildungen, Arch. Math., 11 (1960), 44–49.CrossRefGoogle Scholar
[7] Kerner, H., Über die Automorphismengruppen kompakter komplexer Räume, Arch. Math., 11 (1960), 282–288.CrossRefGoogle Scholar
[8] Morimoto, A., Sur le groupe d’automorphismes d’un espace fibré principal analytique complexe, Nagoya Math. J., 13 (1958), 157–168.CrossRefGoogle Scholar
[9] Remmert, R., Holomorphe und meromorphe Abbildungen komplexer Raume, Math. Ann., 133 (1957), 328–370.CrossRefGoogle Scholar