Greenberg's theorem and equivalence problem on compact Riemann surfaces
Satoru Mizuta and Makoto Namba
Source: Osaka J. Math. Volume 43, Number 1
(2006), 137-178.
Abstract
Another proof of Greenberg's theorem on automorphism groups of compact \mboxRiemann surfaces is given. Using the idea of the proof, the equivalence problem for finite Galois coverings of the compact projective line is answered affirmatively, except special type of coverings.
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Permanent link to this document: http://projecteuclid.org/euclid.ojm/1146242999
Mathematical Reviews number (MathSciNet): MR2222406
Zentralblatt MATH identifier: 1105.14039
References
A.F. Beardon: The Geometry of Discrete Groups, Springer-Verlag, 1983.
Mathematical Reviews (MathSciNet): MR698777
Zentralblatt MATH: 0528.30001
J.S. Birman: Braids, Links, and Mapping Class Groups, Ann. Math. Studies 82, Princeton, 1974.
Mathematical Reviews (MathSciNet): MR375281
R.H. Fox: Covering spaces with singularities: in Lefschetz Symposium, Princeton Univ. Press, 1957, 243--262.
Mathematical Reviews (MathSciNet): MR123298
Zentralblatt MATH: 0079.16505
H. Grauert and R. Remmert: Komplexe Räume, Math. Ann. 136 (1958), 245--318.
Mathematical Reviews (MathSciNet): MR103285
Digital Object Identifier: doi:10.1007/BF01362011
L. Greenberg: Maximal Fuchsian groups, Bull. Amer. Math. Soc. 69 (1963), 569--573.
Mathematical Reviews (MathSciNet): MR148620
Digital Object Identifier: doi:10.1090/S0002-9904-1963-11001-0
Y. Imayoshi and M. Taniguchi: An Introduction to Teichmüller Spaces, Springer-Varlag, 1992.
Mathematical Reviews (MathSciNet): MR1215481
G.A. Jones and D. Singerman: Complex Functions---an Algebraic and Geometric Viewpoint, Cambridge Univ. Press, 1987.
Mathematical Reviews (MathSciNet): MR890746
Zentralblatt MATH: 0608.30001
T. Kato: Conformal equivalence of compact Riemann surfaces, Japan J. Math. 7 (1981), 281--289.
Mathematical Reviews (MathSciNet): MR729439
F. Klein: Gesammelte Mathematische Abhandlungen, Dritter Band, Reprinted by Springer-Verlag, 1973.
T. Matsuno: On a theorem of Zariski-Vankampen type and its applications, Osaka J. Math. 32 (1995), 645--658.
Mathematical Reviews (MathSciNet): MR1367896
D. Mumford, J. Fogarty and F. Kirwan: Geometric Invariant Theory, Third enlarged edition, Springer-Verlag, 1994.
Mathematical Reviews (MathSciNet): MR1304906
M. Namba: Equivalence problem and automorphism groups of certain compact Riemann surfaces, Tukuba J. Math. 5 (1981), 319--338.
Mathematical Reviews (MathSciNet): MR653125
M. Namba: Families of Meromorphic Functions on Compact Riemann Surfaces, Lecture Notes in Math. 767, Springer-Verlag, 1979.
Mathematical Reviews (MathSciNet): MR555241
Zentralblatt MATH: 0417.32008
M. Namba: Branched Coverings and Algebraic Functions, Reseach Notes in Math. 161, Pitman-Longman, 1987.
Mathematical Reviews (MathSciNet): MR933557
Zentralblatt MATH: 0706.14017
G. Pourcin: Théoremè de Douady au-dessus de $S$, Ann. Scuola Norm. Sup. Pisa 23 (1969), 451--459.
Mathematical Reviews (MathSciNet): MR257402
K. Sakurai and M. Suzuki: Equivalence problem and automorphism groups of some Abelian branched coverings of the Riemann sphere, Mem. Kyushu Univ. 42 (1988), 145--152.
Mathematical Reviews (MathSciNet): MR963203
H. Schuster: Zur Theorie der Deformationen kompakter komplexer Räume, Inv. Math. 9 (1970), 284--294.
Mathematical Reviews (MathSciNet): MR268921
Digital Object Identifier: doi:10.1007/BF01425483
H. Völklein: Moduli spaces for covers of the Riemann sphere, Israel J. Math. 85 (1994), 407--430.
Mathematical Reviews (MathSciNet): MR1264353
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