Abstract
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.
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Acknowledgment
The author is grateful to his colleague Angel Carocca who generously told him how to construct Example 2 in Section 7.
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Partially supported by Fondecyt Grant 11180024, Redes Etapa Inicial Grant 2017-170071 and Anillo ACT1415 PIA-CONICYT Grant.
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Reyes-Carocca, S. On Riemann surfaces of genus g with 4g–4 automorphisms. Isr. J. Math. 237, 415–436 (2020). https://doi.org/10.1007/s11856-020-2010-3
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DOI: https://doi.org/10.1007/s11856-020-2010-3