On the Levi problem with singularities

Details On the Levi problem with singularities On the Levi problem with singularities

2001-01-11

arxiv.org/abs/math/0101104v1

Mathematics

Complex Variables

8 pages, no figures, latex

Scientific paper

In section 1, we show that if $X$ is a Stein normal complex space of dimension n and $D\subset \subset X$ an open subset which is the union of an increasing sequence $D_{1}\subset D_{2}\subset ...\subset D_{n}\subset >...$ of domains of holomorphy in $X$. Then $D$ is a domain of holomorphy. In section 2, we prove that a domain of holomorphy $D$ which is relatively compact in a 2-dimensional normal Stein space $X$ itself is Stein. In section 3, we show that if $X$ is a Stein space of dimension n and $D\subset X$ an open subspace which is the union of an increasing sequence $D_{1}\subset D_{2}\subset ...\subset D_{n}\subset ...$ of open Stein subsets of $X$. then $D$ itself is Stein, if $X$ has isolated singularities.

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