标题： 双曲面的对应关系，组合定理和Hurwitz空间 显示英文标题

标题： Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces

摘要： 我们构造了一类在任意亏格的双曲黎曼曲面上的对应关系，这些对应关系结合了有限多个Fuchsian零亏格轨道群和Blaschke乘积。 作为中间步骤，我们首先在黎曼球面上构造这些对象的部分定义映射的解析组合。 然后，我们以双曲对合和紧黎曼曲面上的亚纯映射来对这些解析组合进行代数表征。 这些对合和亚纯映射进而产生所需的对应关系。 此类对应关系的模空间可以与Teichmüller空间和Blaschke空间的乘积相识别。 对应关系的显式描述使我们能够将这个乘积空间自然地注入到适当的Hurwitz空间中。 显示英文摘要

摘要： We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic combinations of these objects as partially defined maps on the Riemann sphere. We then give an algebraic characterization of these analytic combinations in terms of hyperelliptic involutions and meromorphic maps on compact Riemann surfaces. These involutions and meromorphic maps, in turn, give rise to the desired correspondences. The moduli space of such correspondences can be identified with a product of Teichm\"uller spaces and Blaschke spaces. The explicit description of the correspondences then allows us to construct a dynamically natural injection of this product space into appropriate Hurwitz spaces.