OKA PROPERTIES OF SOME HYPERSURFACE COMPLEMENTS

作者：Hanysz Alexander^*

来源：Proceedings of the American Mathematical Society, 2014, 142(2): 483-496.

• Stein manifold
• Oka manifold
• Oka map
• subelliptic manifold
• spray
• hyperbolic manifold
• hypersurface complement
• hyperplane arrangement
• meromorphic function

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.

• 出版日期2014-2