Osaka Journal of Mathematics

The Levi problem for Riemann domains over the blow-up of $\mathbb{C}^{n+1}$ at the origin

Natalia Gaşiţoi

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Abstract

We investigate unbranched Riemann domains $p\colon X \to \tilde{\mathbb{C}}^{n+1}$ over the blow-up of $\mathbb{C}^{n+1}$ at the origin in the case when $p$ is a Stein morphism. We prove that such a domain is Stein if and only if it does not contain an open set $G \subset X$ such that $p|_{G}$ is injective and $p(G)$ contains a subset of the form $W \setminus A$, where $A$ is the exceptional divisor of $\tilde{\mathbb{C}}^{n+1}$ and $W$ is an open neighborhood of $A$.

Article information

Source
Osaka J. Math., Volume 51, Number 3 (2014), 657-665.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1414090796

Mathematical Reviews number (MathSciNet)
MR3272610

Zentralblatt MATH identifier
1302.32012

Subjects
Primary: 32E40: The Levi problem
Secondary: 32D26: Riemann domains

Citation

Gaşiţoi, Natalia. The Levi problem for Riemann domains over the blow-up of $\mathbb{C}^{n+1}$ at the origin. Osaka J. Math. 51 (2014), no. 3, 657--665. https://projecteuclid.org/euclid.ojm/1414090796


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