Abstract
In [2] for the first time there have been given a complete proof of the following statement of A. Hurwitz: For any integer g > 2 there exists a compact Riemann surface of genus g, whose group of all conformai automorphisms is trivial. Then Greenberg [3] has shown that for g > 2 almost all points in the Teichmu̎ller space Tg, except perhaps for an analytic subset, correspond to Riemann surfaces with the trivial group of conformal automorphisms. Nevertheless, only a few constructive examples of such Riemann surfaces are known. One of them is given by Accola [1]. However, the method of Accola does not let us describe analytically the fundamental set of a Fuchsian group which uniformizes that surface. In the present paper, announced in [5], we construct in an explicit way the fundamental set of a Fuchsian group which uniformizes a compact Riemann surface with the trivial group of conformai automorphisms.
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References
ACCOLA, R.D.M.: ‘Strongly branched coverings of closed Riemann surfaces’, Proc. Amer. Math. Soc. 26 no. 2 (1970), 315–322.
BAILY, W.: ‘On the automorphism group of a generic curve of genus > 2’, J. Math. Kyoto Univ. 1 (1961/1962), 101–108;
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© 1989 Kluwer Academic Publishers
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Mednykh, A.D. (1989). Hyperbolic Riemann Surfaces with the Trivial Group of Automorphisms. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_10
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DOI: https://doi.org/10.1007/978-94-009-2643-1_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7693-7
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