Invariance of the parametric Oka property

TL;DR

This paper proves that the parametric Oka property is preserved under certain holomorphic fibrations and establishes a parametric Oka principle for holomorphic liftings, advancing understanding of complex manifold mappings.

Contribution

It demonstrates the invariance of the parametric Oka property under specific holomorphic fibrations and introduces a new parametric Oka principle for liftings.

Findings

POP of B implies POP of E under given conditions

POP of E implies POP of B for contractible parameters

Establishment of a parametric Oka principle for liftings

Abstract

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.