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arXiv · 1802.10025

On the one-dimensional family of Riemann surfaces of genus $q$ with $4q$ automorphisms

Sebastián Reyes-Carocca
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Abstract

Bujalance, Costa and Izquierdo have recently proved that all those Riemann surfaces of genus $g \ge 2$ different from $3, 6, 12, 15$ and 30, with exactly $4g$ automorphisms form an equisymmetric one-dimensional family, denoted by $\mathcal{F}_g.$ In this paper, for every prime number $q \ge 5,$ we explore further properties of each Riemann surface $S$ in $\mathcal{F}_q$ as well as of its Jacobian variety $JS.$

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Sebastián Reyes-Carocca. 2018-02-27. On the one-dimensional family of Riemann surfaces of genus $q$ with $4q$ automorphisms. https://doi.org/10.1016/j.jpaa.2018.07.011

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