Abstract
In this chapter we extend the Oka principle to sections of certain non-locally trivial holomorphic submersions Z→X over a Stein base space X. The main result is a theorem of Gromov (1989) and some of its generalizations. Roughly stated, it says that the existence of a finite dominating family of fiber-sprays on Z over each sufficiently small open subset of X implies all forms of the Oka principle for sections X→Z; the analogous result is proved in the stratified case. We give several examples and applications.
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© 2011 Springer-Verlag Berlin Heidelberg
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Forstnerič, F. (2011). Elliptic Complex Geometry and Oka Principle. In: Stein Manifolds and Holomorphic Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22250-4_6
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DOI: https://doi.org/10.1007/978-3-642-22250-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22249-8
Online ISBN: 978-3-642-22250-4
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