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Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime

Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime
Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime

We classify compact Riemann surfaces of genus g, where g − 1 is a prime p, which have a group of automorphisms of order ρ(g − 1) for some integer ρ ≥ 1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ > 6, and of the first and third authors for ρ = 3, 4, 5 and 6. As a corollary we classify the orientably regular hypermaps (including maps) of genus p + 1, together with the non-orientable regular hypermaps of characteristic −p, with automorphism group of order divisible by the prime p; this extends results of Conder, Širáň and Tucker for maps.

Automorphism group, Compact riemann surface, Dessin d’enfant, Finite group, Hypermap, Jacobian, Map
2737-0690
839-867
Izquierdo, Milagros
77c2c66e-569a-4af8-abc3-37618975287e
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Reyes-Carocca, Sebastián
20f16cac-f0b4-4fc1-be04-a643dc003864
Izquierdo, Milagros
77c2c66e-569a-4af8-abc3-37618975287e
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Reyes-Carocca, Sebastián
20f16cac-f0b4-4fc1-be04-a643dc003864

Izquierdo, Milagros, Jones, Gareth A. and Reyes-Carocca, Sebastián (2021) Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime. Annales Fennici Mathematici, 46 (2), 839-867. (doi:10.5186/aasfm.2021.4649).

Record type: Article

Abstract

We classify compact Riemann surfaces of genus g, where g − 1 is a prime p, which have a group of automorphisms of order ρ(g − 1) for some integer ρ ≥ 1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ > 6, and of the first and third authors for ρ = 3, 4, 5 and 6. As a corollary we classify the orientably regular hypermaps (including maps) of genus p + 1, together with the non-orientable regular hypermaps of characteristic −p, with automorphism group of order divisible by the prime p; this extends results of Conder, Širáň and Tucker for maps.

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Accepted/In Press date: 30 October 2020
Published date: 4 August 2021
Additional Information: Funding Information: Acknowledgment. The authors are grateful to David Singerman for a number of helpful remarks concerning Fuchsian groups, and to an anonymous referee for suggesting some very useful improvements to the paper. The third author was partially supported by Fondecyt Grants 11180024 and 1190991. The first and third authors were partially supported by Redes Grant 170071. Publisher Copyright: © 2021,Annales Fennici Mathematici.All Rights Reserved.
Keywords: Automorphism group, Compact riemann surface, Dessin d’enfant, Finite group, Hypermap, Jacobian, Map

Identifiers

Local EPrints ID: 478552
URI: http://eprints.soton.ac.uk/id/eprint/478552
ISSN: 2737-0690
PURE UUID: 18a5bd14-9a15-4877-a09e-cd98bba66909

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Date deposited: 04 Jul 2023 17:54
Last modified: 05 Jun 2024 19:46

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Contributors

Author: Milagros Izquierdo
Author: Gareth A. Jones
Author: Sebastián Reyes-Carocca

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