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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A relative Oka-Grauert principle for holomorphic submersions over $ 1$-convex spaces


Author: Jasna Prezelj
Journal: Trans. Amer. Math. Soc. 362 (2010), 4213-4228
MSC (2010): Primary 32C15, 32C25, 32L05, 32L10, 32E05, 32E10, 32E30, 32C35
Published electronically: March 23, 2010
MathSciNet review: 2608403
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Abstract: This paper presents the proof of the relative Oka-Grauert principle for holomorphic submersions over $ 1$-convex spaces using conic neighbourhoods of holomorphic sections over $ 1$-convex spaces. A proof of a version of Cartan's Theorem $ A$ for $ 1$-convex spaces is also given.


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Additional Information

Jasna Prezelj
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
Email: jasna.prezelj@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9947-10-04871-3
PII: S 0002-9947(10)04871-3
Keywords: Stein space, $1$-convex space, relative Oka-Grauert principle, conic neighbourhoods
Received by editor(s): August 21, 2007
Received by editor(s) in revised form: June 1, 2008
Published electronically: March 23, 2010
Additional Notes: The author was supported by research program P1 - 0291, Slovenia.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.