Realizability of branched coverings of surfaces

Realizability of branched coverings of surfaces
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表面分支覆盖的可实现性

DOI：
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
R. Stong
R. Stong
中科院分区：
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文献类型：
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作者：
A. Edmonds;R. Kulkarni;R. Stong

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抽象的。闭合表面之间的d度的分支覆盖M N确定d的分区的集合6D-其“分支数据”-对应于分支点的集合。划分的集合必须满足黎曼-赫维茨公式所隐含的某些明显条件。本文研究了在何种程度上任何这样的有限收集6D的分区d可以实现为分支数据的一个适当的分支覆盖。如果N不是2-球面，则这样的数据总是可以实现的。如果6D与d相比包含足够多的元素，那么它可以实现。只要d是非素的，例子就由不可实现的数据构成。
ABSrRACT. A branched covering M N of degree d between closed surfaces determines a collection 6D of partitions of d-its "branch data"-corresponding to the set of branch points. The collection of partitions must satisfy certain obvious conditions implied by the Riemann-Hurwitz formula. This paper investigates the extent to which any such finite collection 6D of partitions of d can be realized as the branch data of a suitable branched covering. If N is not the 2-sphere, such data can always be realized. If 6D contains sufficiently many elements compared to d, then it can be realized. And whenever d is nonprime, examples are constructed of nonrealizable data.