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-problem on weakly 1-complete Kähler manifolds

Published online by Cambridge University Press:  22 January 2016

Hideaki Kazama  and
Shigeharu Takayama
Hideaki Kazama
Affiliation:
Graduate School of Mathematics, Kyushu University, Ropponmatsu Chuo-ku, Fukuoka, 810, Japan
Shigeharu Takayama
Affiliation:
Department of Mathematics, Graduate School of Sciences, Osaka University, Toyonaka, Osaka, 560-0043, Japan
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Abstract

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We consider a problem whether Kodaira’s -Lemma holds on weakly 1-complete Kähler manifolds or not. This problem was proposed by S. Nakano. We prove that the Lemma holds for some class of complex quasi-tori ℂn/Γ, and it does not hold for the other class of them. Every complex quasi-tori is weakly 1-complete and complete Kähler. Then we get a negative answer for the above problem.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 155 , 1999 , pp. 81 - 94
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

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