Invariance of the parametric Oka property

Details Invariance of the parametric Oka property Invariance of the parametric Oka property

2009-01-28

arxiv.org/abs/0901.4373v4

In: P. Ebenfelt, N. Hungerbuehler, J. J. Kohn, N. Mok, E. J. Straube (Eds.), Complex Analysis, pp. 125--143. Trends in Math.,

Mathematics

Complex Variables

Scientific paper

Assume that E and B are complex manifolds and that pi is a holomorphic Serre fibration from E onto E 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.

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