2012/07/31 by Franc Forstnerič, Franc Forstneric, Finnur Lárusson +1 · 8 citations
Mathematics · #Class (philosophy) #Compact space #Complex manifold #Flexibility (engineering) #Geometry and complex manifolds #Holomorphic and Operator Theory #Holomorphic function #Manifold (fluid mechanics) #Meromorphic and Entire Functions #Property (philosophy) #Surface (topology) #math.AG #math.CV #msc:14J28 #msc:32E10 #msc:32E30 #msc:32G05 #msc:32H02 #msc:32J15 #msc:32Q28 #msc:32S45
paper · pdf · doi:10.1093/imrn/rnt044
published in International Mathematics Research Notices 2014(13), 3714-3734 (Oxford University Press) · Version 2: Theorem 11 reformulated and its proof corrected. Minor improvements to the exposition. Version 3: A few minor improvements. To appear in International Mathematics Research Notices
arxiv created 2013/02/21 · openalex publication_date 2013/03/27 · arxiv updated 2014/09/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 , , 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.