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Oka properties of some hypersurface complements


Author: Alexander Hanysz
Journal: Proc. Amer. Math. Soc. 142 (2014), 483-496
MSC (2010): Primary 32Q28; Secondary 14J70, 32H02, 32H04, 32Q45, 32Q55, 52C35
DOI: https://doi.org/10.1090/S0002-9939-2013-11754-5
Published electronically: October 8, 2013
MathSciNet review: 3133990
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Abstract: 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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Additional Information

Alexander Hanysz
Affiliation: School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia
Email: alexander.hanysz@adelaide.edu.au, alexander.hanysz@abs.gov.au

DOI: https://doi.org/10.1090/S0002-9939-2013-11754-5
Keywords: Stein manifold, Oka manifold, Oka map, subelliptic manifold, spray, hyperbolic manifold, hypersurface complement, hyperplane arrangement, meromorphic function
Received by editor(s): December 7, 2011
Received by editor(s) in revised form: March 14, 2012
Published electronically: October 8, 2013
Communicated by: Franc Forstneric
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.