Oka properties of some hypersurface complements

Details Oka properties of some hypersurface complements Oka properties of some hypersurface complements

2011-11-29

arxiv.org/abs/1111.6655v2

Mathematics

Complex Variables

17 pages. Version 2: expanded Example 4.5, other minor improvements. To appear in Proceedings of the American Mathematical Soc

Scientific paper

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.

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