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Type: Journal article
Title: Holomorphic flexibility properties of compact complex surfaces
Author: Forstnerič, F.
Lárusson, F.
Citation: International Mathematics Research Notices, 2014; 2014(13):3714-3734
Publisher: Oxford University Press
Issue Date: 2014
ISSN: 1073-7928
Statement of
Franc Forstnerič, and Finnur Lárusson
Abstract: We introduce the notion of a stratified Oka manifold and prove that such a manifold X is strongly dominable in the sense that, for every x ∈ X, there is a holomorphic map,f:Cn→X,n=dim X, such that f(0)=x and f is a local biholomorphism at 0. We deduce that every Kummer surface is strongly dominable. We determine which minimal compact complex surfaces of class VII are Oka, assuming the global spherical shell conjecture. We deduce that the Oka property and several weaker holomorphic flexibility properties are in general not closed in families of compact complex manifolds. Finally, we consider the behavior of the Oka property under blowing up and blowing down.
Rights: © The Author(s) 2013
DOI: 10.1093/imrn/rnt044
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