A Hyperelliptic View on Teichmuller Space. II

Teichmüller 空间的角参数化与超椭圆曲面

Angle Parametrization of Teichmüller space and hyperelliptic surfaces

本文通过角参数对 Teichmüller 空间及超椭圆曲面空间进行参数化，分别给出 $6g-5$ 和 $4g-2$ 个参数，并证明了相应结果。

A Hyperelliptic View on Teichmuller Space. I

We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces in terms of natural and effective coordinates as the space of certain (2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We essentially use the concept of a simple earthquake which is a particular case of a Fenchel-Nielsen twist deformation. Such earthquakes generate a group that acts transitively on TH_n. This fact can be interpreted as a continuous analog of the well-known Dehn theorem saying that the mapping class group is generated by Dehn twists. We find a simple and effective criterion t…

Length series on Teichmuller space

We prove that a certain series defines a constant function using Wolpert's formula for the variation of the length of a geodesic along a Fenchel Nielsen twist. Subsequently we determine the value viewing it as function on the the Deligne Mumford compactification and evaluating it at the stable curve at infinity.

Dehn twist presentations of hyperelliptic periodic diffeomorphisms on closed surfaces

We classify up to conjugacy the group generated by a commuting pair of a periodic diffeomorphism and a hyperelliptic involution on an oriented closed surface. This result can be viewed as a refinement of Ishizaka's result on classification of the mapping classes of hyperelliptic periodic diffeomorphisms. As an application, we obtain the Dehn twist presentations of hyperelliptic periodic mapping classes, which are closely related to the ones obtained by Ishizaka.

双曲面上的对应、组合定理与赫维茨空间

Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces

本文构造了任意亏格双曲黎曼曲面上结合零亏格富克斯群与布拉施克乘积的对应，给出其解析组合的代数刻画，识别对应模空间为泰希米勒空间与布拉施克空间的乘积，并构造该乘积空间到赫维茨空间的动态自然单射。

Amoebas, tropical varieties and compactification of Teichmuller spaces

In this paper we try to look at the compactification of Teichmuller spaces from a tropical viewpoint. We describe a general construction for the compactification of algebraic varieties, using their amoebas, and we describe the boundary via tropical varieties. When we apply this construction to the Teichmuller spaces we see that they can be mapped in a real algebraic hypersurface in such a way that the cone over the boundary is a subpolyhedron of a tropical hypersurface. We want to show how some properties of the boundary becomes straightforward if looked at from this point of view. For example…