2011/11/29 by Alexander Hanysz, Hanysz, Alexander · 1 citation
Mathematics · #32H02 #32H04 #32Q28 (Primary) 14J70 #32Q45 #32Q55 #52C35 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:14J70 #msc:32H02 #msc:32H04 #msc:32Q28 #msc:32Q45 #msc:32Q55 #msc:52C35
paper · pdf · doi:10.48550/arxiv.1111.6655
17 pages. Version 2: expanded Example 4.5, other minor improvements. To appear in Proceedings of the American Mathematical Society
openalex publication_date 2011/11/29 · arxiv created 2012/04/19 · arxiv updated 2012/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Oka manifolds can be viewed as the "opposite" of Kobayashi hyperbolic manifolds. Kobayashi asked whether the complement in projective space of a generic hypersurface of sufficiently high degree is hyperbolic. Therefore it is natural to investigate Oka properties of complements of low degree hypersurfaces. We determine which complements of hyperplane arrangements in projective space are Oka. A related question is which hypersurfaces in affine space have Oka complements. We give some results for graphs of meromorphic functions.