On Dihedral Group Actions on Riemann Surfaces

Pablo Alvarado-Seguel, Sebastián Reyes-Carocca
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Abstract

This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is obtained. Second, a refinement of a result of Bujalance, Cirre, Gamboa and Gromadzki about signature realization is provided. Finally, we apply our results to isogeny decompositions of Jacobians by Prym varieties and by elliptic curves, extending results of Carocca, Recillas and Rodr\'iguez. In particular, we give a complete classification of Jacobians with dihedral action whose group algebra decomposition induces a decomposition into factors of the same dimension.
论黎曼曲面上的二面群作用
本文讨论紧凑黎曼曲面上的二面体群作用以及与之相关的不同几何数据之间的相互作用。首先,获得了几何特征与解析描述之间的客观对应关系。其次,对 Bujalance、Cirre、Gamboa 和 Gromadzki 关于签名实现的结果进行了改进。最后,我们将我们的结果应用于雅各布数在普莱姆变种和椭圆曲线上的同源分解,扩展了卡罗卡、雷西拉斯和罗德里格斯的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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