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arXiv 0901.43732009-01math.CV

参数Oka性质的不变性

Invariance of the parametric Oka property

Franc Forstneric

发表信息：: In: P. Ebenfelt, N. Hungerbuehler, J. J. Kohn, N. Mok, E. J. Straube (Eds.), Complex Analysis, pp. 125--143. Trends in Math., Birkhauser, 2010

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摘要：

设E和B是复流形，π是从E到E的全纯Serre纤维化，使得E在B中任意点的一个小邻域上存在一个全纯纤维喷簇的有限控制族.我们证明了B的参数Oka性质（POP）蕴涵E的POP;反之，对于可收缩参数空间，E的POP蕴涵B的POP.这遵循我们在论文中建立的全纯提升的参数Oka原理。

英文摘要：

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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