Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/96211
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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 1687-0247 |
Statement of Responsibility: | 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 |
Published version: | http://dx.doi.org/10.1093/imrn/rnt044 |
Appears in Collections: | Aurora harvest 7 Mathematical Sciences publications |
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RA_hdl_96211.pdf Restricted Access | Restricted Access | 154.68 kB | Adobe PDF | View/Open |
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