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Mathematische Zeitschrift

, Volume 272, Issue 3–4, pp 1051–1058 | Cite as

Deformations of Oka manifolds

  • Finnur Lárusson
Article

Abstract

We investigate the behaviour of the Oka property with respect to deformations of compact complex manifolds. We show that in a family of compact complex manifolds, the set of Oka fibres corresponds to a G δ subset of the base. We give a necessary and sufficient condition for the limit fibre of a sequence of Oka fibres to be Oka in terms of a new uniform Oka property. We show that if the fibres are tori, then the projection is an Oka map. Finally, we consider holomorphic submersions with noncompact fibres.

Keywords

Oka manifold Convex approximation property Oka map Deformation 

Mathematics Subject Classification (2010)

Primary 32G05 Secondary 32E10 32Q28 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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