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On Symmetries Of Compact Riemann Surfaces With Cyclic Groups Of Automorphisms

Gamboa Mutuberria, José Manuel and Bujalance, E. and Cirre, J.F. and Gromadzki, G. (2006) On Symmetries Of Compact Riemann Surfaces With Cyclic Groups Of Automorphisms. Revista Matemática Iberoamericana, 301 (1). pp. 82-95. ISSN 0213-2230

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Abstract

A Riemann surface X is said to be of type (n,m) if its full automorphism group AutX is cyclic of order n and the quotient surface X/AutX has genus m. In this paper we determine necessary and sufficient conditions on the integers n,m,g and γ, where n is odd, for the existence of a Riemann surface of genus g and type (n,m) admitting a symmetry with γ ovals.

Item Type:Article
Uncontrolled Keywords:Riemann surface; automorphism group; Fuchsian and nec groups; symmetry; ovals
Subjects:Sciences > Mathematics > Functions
ID Code:15234
References:

E. Bujalance, M.D.E. Conder, On cyclic groups of automorphisms of Riemann surfaces, J. London Math. Soc. (2) 59 (1999) 573–584.

E. Bujalance, A.F. Costa, J.M. Gamboa, Real parts of complex algebraic curves, in: Real Analytic and Algebraic Geometry, Trento, 1988, in: Lecture Notes in Math., vol. 1420, Springer-Verlag, Berlin, 1990, pp. 81–110.

E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, Lecture Notes in Math., vol. 1439, Springer-Verlag, Berlin, 1990.

G. Gromadzki, On a Harnack–Natanzon theorem for the family of real forms of Riemann surfaces, J. Pure Appl. Algebra 121 (1997) 253–269.

G. Gromadzki, Symmetries of Riemann surfaces from a combinatorial point of view, in: Topics of Riemann Surfaces and Fuchsian Groups, in: London Math. Soc. Lecture Note Ser., vol. 287, Cambridge Univ. Press, 2001, pp. 91–112.

A. Harnack, Über die Vieltheiligkeit der ebenen algebraischen Kurven, Math. Ann. 10 (1876) 189–198.

W.J. Harvey, Cyclic groups of automorphisms of a compact Riemann surface, Quart. J. Math. 17 (1966) 86–97.

A.H.M. Hoare, D. Singerman, The orientability of subgroups of plane groups, in: Groups—St. Andrews 1981, St. Andrews, 1981, in: London Math. Soc. Lecture Note Ser., vol. 71, Cambridge Univ. Press, 1982, pp. 221–227.

G. Nakamura, The existence of symmetric Riemann surfaces determined by cyclic groups, Nagoya Math. J. 151 (1998) 129–143.

S.M. Natanzon, Klein surfaces, Uspekhi Mat. Nauk 45 (6(276)) (1990) 47–90, 189 (in Russian); translation in Russian Math. Surveys 45 (6) (1990) 53–108.

S.M. Natanzon, Geometry and algebra of real forms of complex curves, Math. Z. 243 (2) (2003) 391–407.

D. Singerman, Finitely maximal Fuchsian groups, J. London Math. Soc. (2) 6 (1972) 29–38.

D. Singerman, On the structure of non-euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974) 233–240.

Deposited On:17 May 2012 08:37
Last Modified:06 Feb 2014 10:19

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