Geodesic
Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime
Milagros Izquierdo1 ; Gareth A. Jones2 ; Sebastián Reyes-Carocca3
1 Linköping University, Department of Mathematics
2 University of Southampton, School of Mathematical Sciences
3 Universidad de La Frontera, Departamento de Matemática y Estadística
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 839-867.

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We classify compact Riemann surfaces of genus $g$, where $g-1$ is a prime $p$, which have a group of automorphisms of order $\rho(g-1)$ for some integer $\rho\ge 1$, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for $\rho>6$, and of the first and third authors for $\rho=$ 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.
Keywords: Compact Riemann surface, automorphism group, finite group, Jacobian, map, hypermap, dessin d'enfant

Milagros Izquierdo 1 ; Gareth A. Jones 2 ; Sebastián Reyes-Carocca 3

1 Linköping University, Department of Mathematics
2 University of Southampton, School of Mathematical Sciences
3 Universidad de La Frontera, Departamento de Matemática y Estadística 
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Milagros Izquierdo; Gareth A. Jones; Sebastián Reyes-Carocca. Groups of automorphisms of Riemann surfaces and maps  of genus p + 1 where p is prime. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 839-867. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a15/