论文标题
在Riemann表面上的大型主要动作
On large prime actions on Riemann surfaces
论文作者
论文摘要
在本文中，我们研究了$ g $属的紧凑型黎曼表面，并具有质量订单$ g+1的自动形态。$主要结果提供了此类表面的分类。此外，我们将它们描述为代数曲线，确定并实现其完整的自动形态群体并计算其模量领域。我们还研究了它们的雅各布品种的某些方面，例如等级分解和复杂的繁殖。最后，我们确定了四属的Accola-Maclachlan曲线的周期矩阵。
In this article we study compact Riemann surfaces of genus $g$ with an automorphism of prime order $g+1.$ The main result provides a classification of such surfaces. In addition, we give a description of them as algebraic curves, determine and realise their full automorphism groups and compute their fields of moduli. We also study some aspects of their Jacobian varieties such as isogeny decompositions and complex multiplication. Finally, we determine the period matrix of the Accola-Maclachlan curve of genus four.
