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

Kirjoittajat

  • Milagros Izquierdo Linköping University, Department of Mathematics
  • Gareth A. Jones University of Southampton, School of Mathematical Sciences
  • Sebastián Reyes-Carocca Universidad de La Frontera, Departamento de Matemática y Estadística

Avainsanat:

Compact Riemann surface, automorphism group, finite group, Jacobian, map, hypermap, dessin d'enfant

Abstrakti

We classify compact Riemann surfaces of genus g, where g1 is a prime p, which have a group of automorphisms of order ρ(g1) for some integer ρ1, 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.
Osasto
Articles

Julkaistu

2021-08-04

Viittaaminen

Izquierdo, M., Jones, G. A., & Reyes-Carocca, S. (2021). Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime. Annales Fennici Mathematici, 46(2), 839–867. Noudettu osoitteesta https://afm.journal.fi/article/view/110603