Gamboa Mutuberria, José Manuel and Bujalance, E. and Cirre, F.J. and Gromadzki, G. (2003) On Compact Riemann Surfaces With Dihedral Groups Of Automorphisms. Mathematical Proceedings , 134 (3). pp. 465-477. ISSN 0305-0041
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Official URL: http://journals.cambridge.org/abstract_S030500410200662X
We study compact Riemann surfaces of genus g 2 having a dihedral group of automorphisms. We find necessary and sufficient conditions on the signature of a Fuchsian group for it to admit a surface kernel epimorphism onto the dihedral group DN.
The question of extendability of the action of DN is considered.
We also give an explicit parametrization of the moduli space of Riemann surfaces with maximal dihedral symmetry, showing that it is a one-dimensional complex manifold.
Defining equations of all such surfaces and the formulae of their automorphisms are calculated.
The locus of this moduli space consisting of those surfaces admitting some real structure is determined.
|Uncontrolled Keywords:||Riemann surfaces; automorphism groups; moduli space|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
G. A. Adel. Some results on groups related to compact Riemann surfaces. PhD Thesis. University of Minnesota (1983).
T. Breuer. Characters and automorphisms groups of compact Riemann surfaces. London Math. Soc. Lecture Notes Series, 280 (Cambridge University Press, 2000).
E. Bujalance, F. J. Cirre and M. D. E. Conder. On extendability of group actions on compact Riemann surfaces. Trans. Amer. Math. Soc. 355 (2003), 1537–1557.
E. Bujalance, F. J. Cirre, J. M. Gamboa and G. Gromadzki. Symmetry types of hyperelliptic Riemann surfaces. Memoires de la Soci´et´e Math´ematique de France, No 86 (2001).
E. Bujalance and M. D. E. Conder. On cyclic groups of automorphisms of Riemann surfaces. J. London Math. Soc. (2) 59 (1999), 573–584.
E. Bujalance, J. M. Gamboa and G. Gromadzki. The full automorphism groups of hyperelliptic Riemann surfaces Manuscripta Math. 79 (1993) 267–282.
F. J. Cirre. On the birational classification of hyperelliptic real algebraic curves in terms of their equations. Submitted for publication.
G. Gonz´alez-D´ıez andW. J. Harvey. Moduli of Riemann surfaces with symmetry. In Discrete groups and geometry(Birmingham, 1991), 75–93, London Math. Soc. Lecture Notes Series, 173 (Cambridge University Press, 1992).
G. Gonz´alez-D´ıez and R. Hidalgo. Conformal versus topological conjugacy of automorphisms of compact Riemann surfaces Bull. London Math. Soc. 29 (1997), 280–284.
L. Greenberg. Maximal Fuchsian groups. Bull. Amer. Math. Soc. 69 (1963), 569–573.
W. J. Harvey. Cyclic groups of automorphisms of a compact Riemann surface. Quart. J. Math. Oxford 17 (1966), 86–97.
M. Izquierdo. On Klein surfaces and dihedral groups. Math. Scand. 76 (1995), no. 2, 221–232.
C. Maclachlan. Abelian groups of automorphisms of compact Riemann surfaces Proc. London Math. Soc. (3) 15 (1965), 699–712.
C. Maclachlan. Groups of automorphisms of compact Riemann surfaces. PhD Thesis. University of Birmingham (1966).
C. Maclachlan. Smooth coverings of hyperelliptic surfaces. Quart. J. Math. Oxford (2) (1971), 22, 117–123.
S. Nag. The complex analytic theory of Teichm¨ uller spaces(Wiley, 1988).
K. Nakagawa. On the orders of automorphisms of a closed Riemann surface. Pacific J. Math. (2) 115 (1984), 435–443.
D. Singerman. Finitely maximal Fuchsian groups. J. London Math. Soc. (2) 6 (1972), 29–38.
D. Singerman. Symmetries of Riemann surfaces with large automorphism group. Math. Ann. 210 (1974), 17–32.
|Deposited On:||18 May 2012 09:28|
|Last Modified:||06 Feb 2014 10:19|
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