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In this chapter we prove theorems related to the failure and the restricted validity of the Gromov-Oka Principle for bundles whose fibers are Riemann surfaces of type \((1,1)\) (in other words, the fibers are once punctured tori). The problem can be reduced to the respective problem for \((0,4)\) -bundles (and, hence, for mappings into \(\mathfrak {P}_3\) ) by considering double branched coverings.

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Gromov’s Oka Principle for \((\mathsf {g},\mathsf {m})\) -Fiber Bundles

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  • 发表日期：

    2025年

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  • Burglind Jöricke

摘要

In this chapter we prove theorems related to the failure and the restricted validity of the Gromov-Oka Principle for bundles whose fibers are Riemann surfaces of type \((1,1)\) (in other words, the fibers are once punctured tori). The problem can be reduced to the respective problem for \((0,4)\) -bundles (and, hence, for mappings into \(\mathfrak {P}_3\) ) by considering double branched coverings.