On large prime actions on Riemann surfaces-Reference-Cited by-同舟云学术

On large prime actions on Riemann surfaces

Published:2022-03-31 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Reyes-Carocca Sebastián¹,Rojas Anita M.²

Affiliation:

1. Departamento de Matemática y Estadística , Universidad de La Frontera , Avenida Francisco Salazar 01145 , Temuco , Chile

2. Departamento de Matemáticas , Facultad de Ciencias , Universidad de Chile , Las Palmeras 3425, Ñuñoa , Santiago , Chile

Abstract

Abstract In this article, we study compact Riemann surfaces of genus 𝑔 with an automorphism of prime order g + 1

g+1

. 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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2020-0140/pdf

Reference73 articles.

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2. R. Accola, Topics in the Theory of Riemann Surfaces, Lecture Notes in Math. 1595, Springer, Berlin, 1994.

3. N. Arakelian and P. Speziali, Algebraic curves with automorphism groups of large prime order, Math. Z. 299 (2021), no. 3–4, 2005–2028.

4. E. Badr and F. Bars, Plane model-fields of definition, fields of definition, and the field of moduli for smooth plane curves, J. Number Theory 194 (2019), 278–283.

5. P. Barraza and A. M. Rojas, The group algebra decomposition of Fermat curves of prime degree, Arch. Math. (Basel) 104 (2015), no. 2, 145–155.

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