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Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9557-9566
University of Southampton, Southampton, UK.
Universidad de La Frontera, Araucanía, Chile.
2020 (English)In: Annales Academiæ Scientiarum Fennicæ Mathematica, ISSN 1239-629X, Vol. 46, no 2, p. 839-867Article in journal (Refereed) Published
Abstract [en]

We classify compact Riemann surfaces of genus g, where g−1 is a prime p, whichhave 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.

Place, publisher, year, edition, pages
Helsinki, Finland: Academia Scientiarum Fennica , 2020. Vol. 46, no 2, p. 839-867
Keywords [en]
Compact Riemann surface, automorphism group, finite group, Jacobian, map, hypermap, dessin d’enfant
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-172024DOI: 10.5186/aasfm.2021.4649Scopus ID: 2-s2.0-85114837063OAI: oai:DiVA.org:liu-172024DiVA, id: diva2:1511321
Available from: 2020-12-18 Created: 2020-12-18 Last updated: 2022-11-28

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Izquierdo, Milagros

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Izquierdo, MilagrosReyes Carocca, Sebastián
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CiteExportLink to record
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Citation style
  • apa
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  • Other locale
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Output format
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