Angle Parametrization of Teichmüller space and hyperelliptic surfaces

Abstract

Let $S_g$ be a closed orientable surface of genus $g \geq 2$, and let $\mathcal{T}_g$ be the Teichmüller space of $S_g$. Let $\mathcal{H}_g$ denotes the space of all hyperelliptic surfaces of genus $g$. For $g\geq 3$, we have proved that $\mathcal{T}_g$ can be parametrized by $6g-5$ angle parameters. We also prove that for $g\geq 2$, $\mathcal{H}_g$ can be parametrized by $4g-2$ angle parameters.

Figures (9)

• Figure 1: A canonical polygon $P(2).$
• Figure 2:
• Figure 3: Triangle.
• Figure 4:
• Figure 5:

Theorems & Definitions (22)

• Theorem 1.1
• Theorem 1.2
• Definition 2.2
• Theorem 2.3
• Definition 2.4
• Definition 2.5
• Remark 2.6
• Theorem 2.7
• Remark 2.8
• Definition 2.10