全纯凸流形上的局部Stein域

Q2 Mathematics

Journal of Mathematics of Kyoto University Pub Date : 2008-01-01 DOI:10.1215/KJM/1250280978

V. Vâjâitu

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引用次数: 2

摘要

设π: Y−→X是复空间X上的定义域。假设π是局部斯坦因。然后，我们证明了Y是Stein，条件是X是Stein，并且存在一个包含X sing与π−1 (W) Stein的开集W，或者π在X sing中任意点上是局部超凸的。同样地，我们证明，如果X是q完备的，并且X有孤立的奇点，那么Y是q完备的。

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Locally Stein domains over holomorphically convex manifolds

Let π : Y −→ X be a domain over a complex space X . Assume that π is locally Stein. Then we show that Y is Stein provided that X is Stein and either there is an open set W containing X sing with π − 1 ( W ) Stein or π is locally hyperconvex over any point in X sing . In the same vein we show that, if X is q -complete and X has isolated singularities, then Y results q -complete.

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来源期刊

Journal of Mathematics of Kyoto University 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

期刊介绍： Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.