论文标题
一般折纸的Veech组和GALOIS不变的计算
Calculation of Veech groups and Galois invariants of general origamis
论文作者
论文摘要
Teichmüller曲线的非平凡示例已被系统地研究了仿射同构的组合概念不变的概念。折纸（平方砖表面）诱导Teichmüller曲线，绝对Galois组在模量空间中的嵌入曲线上作用。在本文中，我们研究了一般折纸，不承认纯半翻译结构。这种平坦的表面由折纸的切割结构（是翻译表面）给出的。我们提出了一种用于同时计算给定程度折纸的算法。我们已经计算了等价类，$ psl（2，\ mathbb {z}）$ orbits和一些galois不变性，用于$ d \ leq 7 $的折纸折纸的所有模式。
Nontrivial examples of Teichmüller curves have been studied systematically with notions of combinatorics invariant under affine homeomorphisms. An origami (square-tiled surface) induces a Teichmüller curve for which the absolute Galois group acts on the embedded curve in the moduli space. In this paper, we study general origamis not admitting pure half-translation structure. Such a flat surface is given by a cut-and-paste construction from origami that is a translation surface. We present an algorithm for the simultaneous calculation of the Veech groups of origamis of given degree. We have calculated the equivalence classes, the $PSL(2,\mathbb{Z})$-orbits, and some Galois invariants for all the patterns of origamis of degree $d\leq 7$.
