On Riemann surfaces of genus $g$ with $4g-4$ automorphisms

Sebastián Reyes-Carocca

Published 2018-12-03Version 1

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order; namely, compact Riemann surfaces of genus $g$ with a group of automorphisms of order $4g-4.$ Under the assumption that $g-1$ is prime, we provide a complete classification of them and determine isogeny decompositions of the corresponding Jacobian varieties.