Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T17:36:46.576Z Has data issue: false hasContentIssue false

On the stability of pseudoconvexity for certain covering spaces

Published online by Cambridge University Press:  22 January 2016

Takeo Ohsawa*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan, ohsawa@math.nagoya-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that, if is a proper holomorphic map with one-dimensional fibers and a covering map, a point tT has a neighbourhood U such that is holomorphically convex if and only if is holomorphically convex.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[D-G] Docquier, F. and Grauert, H., Levisches Problem und Rungescher Satz für Teilge-biete Steinscher Mannigfaltigkeiten, Math. Ann., 140 (1960), 94123.Google Scholar
[G] Garuert, H., On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math., 68 (1958), 460472.Google Scholar
[N] Nakamura, I., On complex parallelisable manifolds and their small deformations, Proc. Japan Acad., 48 (1972), 447449.Google Scholar
[Nr] Narasimhan, R., The Levi problem for complex spaces II, Math. Ann., 146 (1962), 195216.Google Scholar
[O-1] Ohsawa, T., Completeness of noncompact analytic spaces, Publ. RIMS, Kyoto Univ., 20 (1984), 683992.Google Scholar
[O-2] Ohsawa, T., A note on the variation of Riemann surfaces, Nagoya Math. J., 142 (1996), 14.Google Scholar