The full automorphism groups of hyperelliptic Riemann surfaces
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Abstract
For every integer g≥2 we obtain the complete list of groups acting as the full automorphisms groups on hyperelliptic Riemann surfaces of genus g.
1985 AMS subject classification
Primary 20H10 30F10Key words and phrases
Hyperelliptic Riemann surfaces automorphisms groupsPreview
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References
- [1]A.F. Beardon,A primer on Riemann surfaces, London Math. Soc. Lect. Note Series78 (1984)Google Scholar
- [2]L. Bers,Universal Teichmüller space, Conference of complex analysis methods in physics. University of Indiana, June (1968)Google Scholar
- [3]O. Bolza, On binary sextics with linear transformations into themselves, Amer. J. Math.10 (1888), 47–70MathSciNetCrossRefMATHGoogle Scholar
- [4]R. Brandt, H. Stichtenoth, Die automorphismengruppen hyperelliptischer Kurven, Manuscripta Math55 (1986), 83–92MathSciNetCrossRefMATHGoogle Scholar
- [5]S.A. Broughton, Classifying finite group actions on surfaces of low genus, J. Pure Appl. Algebra69 (1990), 233–270MathSciNetCrossRefMATHGoogle Scholar
- [6]E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki,Automorphism groups of compact bordered Klein surfaces.A combinatorial approach, Lect. Notes in Math1439, Springer-Verlag (1990)Google Scholar
- [7]A. Duma, W. Radtke, Automorphismen und Modulraum Galoisscher dreiblättriger Überlagerungen, Manuscripta Math.50 (1985), 215–228MathSciNetCrossRefMATHGoogle Scholar
- [8]C. Earle, Reduced Teichmüller spaces, Trans. Amer. Math. Soc.126 (1967), 54–63MathSciNetMATHGoogle Scholar
- [9]W.D. Geyer, Invarianten binärer Formen; in: Classification of algebraic varieties and compact complex manifolds, Lecture Notes in Math.412, 36–69 Springer-Verlag, 1974Google Scholar
- [10]L. Greenberg, Maximal Fuchsian groups. Bull. Amer. Math. Soc.69 (1963), 569–573MathSciNetCrossRefMATHGoogle Scholar
- [11]P. Henn, Dissertation, Heidelberg, 1975Google Scholar
- [12]A. Hurwitz, Über algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann.41 (1893), 402–442MathSciNetMATHGoogle Scholar
- [13]T. Kato, On the order of the automorphism group of a compact bordered Riemann surface of genus four, Kodai Math. J. 7 (1984), 120–132MathSciNetCrossRefMATHGoogle Scholar
- [14]K. Komiya, A. Kuribayashi, On the structure of the automorphism group of a compact Riemann surface of genus 3. Algebraic Geometry, 253–299, Summer Meeting 1978, Copenhagen, Lecture Notes in Math.732, Springer-Verlag 1979Google Scholar
- [15]A.M. Macbeath,Discontinuous groups and birational transformations, Proc. of Dundee Summer School, Univ of St. Andrews (1961)Google Scholar
- [16]C. Maclachlan, Maximal normal Fuchsian groups. Illinois J. Math.15 (1971), 104–113MathSciNetMATHGoogle Scholar
- [17]C. Maclachlan, Smooth coverings of hyperelliptic surfaces. Quart. J. Math. Oxford (2)22 (1971), 117–123MathSciNetCrossRefMATHGoogle Scholar
- [18]D. Singerman, Subgroups of Fuchsian groups and finite permutation groups, Bull London Math Soc.2 (1970), 319–323MathSciNetCrossRefMATHGoogle Scholar
- [19]D. Singerman, Finitely maximal Fuchsian groups. J. London Math. Soc. (2)6 (1972), 29–38MathSciNetCrossRefMATHGoogle Scholar
- [20]A. Wiman, Über die hyperelliptischen Kurven und diejenigen vom Geschlecht p=3, welche eindeutigen Transformationen in sich zulassen, Bihang Till. Kongl. Svenska Vetenskaps Akademiens Handlingar21, 1, no-3 (1895)Google Scholar
- [21]H. Zieschang,Surfaces and planar discontinuous groups, Lect. Notes in Math.835, Springer-Verlag (1980)Google Scholar
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