球面圆锥度量与分支覆盖的可实现性
Spherical conic metrics and realizability of branched covers
摘要：
Riemann曲面之间的分支覆盖与某些组合数据相关联，Hurwitz存在性问题是关于满足这些组合约束的给定数据是否可以由某些分支覆盖来实现。我们连接最近的发展在球面圆锥度量这个老问题，并给出了一个新的方法，发现异常（不可实现）的分支数据。作为一个应用，我们发现新的无限集例外分支覆盖黎曼球面上的数据。
英文摘要：
Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new method of finding exceptional (unrealizable) branching data. As an application, we find new infinite sets of exceptional branched cover data on the Riemann sphere.
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