Invariance of the Parametric Oka Property

  • Franc Forstnerič
Part of the Trends in Mathematics book series (TM)


Assume that E and B are complex manifolds and that π : EB is a holomorphic Serre fibration such that E admits a finite dominating family of holomorphic fiber-sprays over a small neighborhood of any point in B. We show that the parametric Oka property (POP) of B implies POP of E; conversely, POP of E implies POP of B for contractible parameter spaces. This follows from a parametric Oka principle for holomorphic liftings which we establish in the paper.


Oka principle Stein spaces subelliptic submersions 

Mathematics Subject Classification (2000)

32E10 32E30 32H02 


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© Springer Basel AG 2010

Authors and Affiliations

  • Franc Forstnerič
    • 1
    • 2
  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia

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