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On Riemann surfaces with 4g automorphisms
Departamento de Matematicas Fundamentales, UNED.
Departamento de Matematicas Fundamentales, UNED.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9557-9566
2017 (English)In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 218, no 1, 18Article in journal (Refereed) Published
Abstract [en]

We determine, for all genus g≥2g≥2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g  ≠ 3,6,12,153,6,12,15 or 30, these surfaces form a real Riemann surface FgFg in the moduli space MgMg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the family. Furthermore we determine the topological types of the real forms of real Riemann surfaces in FgFg. The set of real Riemann surfaces in FgFg consists of three intervals its closure in the Deligne–Mumford compactification of MgMg is a closed Jordan curve. We describe the nodal surfaces that are limits of real Riemann surfaces in Fg

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 218, no 1, 18
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-136286DOI: 10.1016/j.topol.2016.12.013ISI: 000393265500001OAI: oai:DiVA.org:liu-136286DiVA: diva2:1087197
Available from: 2017-04-06 Created: 2017-04-06 Last updated: 2017-04-27

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The full text will be freely available from 2018-12-23 11:26
Available from 2018-12-23 11:26

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