On large prime actions on Riemann surfaces
Algebraic Geometry
2022-01-25 v2
Abstract
In this article we study compact Riemann surfaces of genus with an automorphism of prime order 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.
Cite
@article{arxiv.2009.04596,
title = {On large prime actions on Riemann surfaces},
author = {Sebastián Reyes-Carocca and Anita M. Rojas},
journal= {arXiv preprint arXiv:2009.04596},
year = {2022}
}
Comments
To appear in Journal of Group Theory, 37 pages