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Groups of Automorphisms of Riemann Surfaces and Maps of Genus p+1 Where p is Prime

Authors
  • Izquierdo, Milagros
  • Jones, Gareth A.
  • Reyes-Carocca, Sebastián
Publication Date
Jan 01, 2021
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

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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