论文标题
尼斯怪物上的dessins d'Enfants和一些全体形状结构
Dessins d'enfants and some holomorphic structures on the Loch Ness Monster
论文作者
论文摘要
Dessin d'Enfant的经典理论是在紧凑的定向表面上的两部分地图，是用于研究紧凑的Riemann表面与理性数字领域的绝对Galois组之间的分支覆盖物的组合物体。在本文中，我们展示了该理论如何自然地扩展到不可压缩的定向表面，尤其是我们观察到，尼斯尼斯怪物（Infinite Genus of Ind End的无限属的表面）承认了许多无限的常规Dessins d'Enfant（手性或反射性）。此外，我们在尼斯尼斯怪物上研究了不同的全态结构，该结构来自紧凑型Riemann表面，无限的高纤维化和无限的超椭圆形曲线的同源性覆盖物。
The classical theory of dessin d'enfants, which are bipartite maps on compact orientable surfaces, are combinatorial objects used to study branched covers between compact Riemann surfaces and the absolute Galois group of the field of rational numbers. In this paper, we show how this theory is naturally extended to non-compact orientable surfaces and, in particular, we observe that the Loch Ness monster (the surface of infinite genus with exactly one end) admits infinitely many regular dessins d'enfants (either chiral or reflexive). In addition, we study different holomorphic structures on the Loch Ness monster, which come from homology covers of compact Riemann surfaces, infinite hyperelliptic and infinite superelliptic curves.
