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

2020/03/10 by Izquierdo, Milagros, Jones, Gareth A., Reyes-Carocca, Sebastián · 2 citations
#14H57 #20B25 #20H10 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Primary 30F10 #secondary 11G32

paper · doi:10.48550/arxiv.2003.05017

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, \v Sirá\v n and Tucker for maps.

Cited by

• On orientably-regular maps of Euler characteristic -2p²
• The Hurwitz problem for abelian differentials

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