Abstract
We study the Kobayashi pseudodistance for orbifolds, proving an orbifold version of Brody’s theorem and classifying which one-dimensional orbifolds are hyperbolic.
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Bogomolov, F.; Tschinkel, Y.: Special elliptic fibrations. in Volume of the Fano Conference (Torino 2000). A. Conte Ed. (Also on math AG/ 03)
Brody R.: Compact manifolds and hyperbolicity. T.A.M.S. 235, 213–219 (1978)
Bundgaard S., Nielsen J.: On normal subgroups with finite index in F-groups. Mat. Tidsskr. B. 1951, 56–58 (1951)
Campana F.: Orbifolds, Special Varieties and Classification Theory. Ann. Inst. Fourier 54, 499–665 (2004) (also on mathAG/0110051)
Campana, F.: Orbifoldes spéciales et classification biméromorphe des variétés Kählériennes compactes (arXiv.math 0705.0737)
Campana F.: Fibres multiples sur les surfaces: aspects arithmétiques et hyperboliques. Man. Math. 117, 429–461 (2005) (also on arXiv math. AG)
Campana F., Paun M.: Variétés faiblement spéciales à courbes entières dégénérées. Comp. Math. 143, 95–111 (2007) (also on math. AG)
Darmon H.: Faltings plus epsilon, Wiles plus epsilon and the generalized Fermat equation. C. R. Math. Rep. Acad. Sci. Canada 19(1), 3–14 (1997) Corrigendum no. 2, p. 64
Fox R.: On Fenchel’s conjecture about F-groups. Mat. Tidsskr. B. 1952, 61–65 (1952)
Harris J., Tschinkel Y.: Rational points on quartics. Duke Math. J. 104, 477–500 (2000)
Kobayashi S.: Hyperbolic Complex Spaces. Springer, Berlin (1998)
Lang S.: Introduction to Complex Hyperbolic Spaces. Springer, Berlin (1987)
Lang, S.: Number Theory III. Diophantine geometry. Encyclopaedia of Mathematical Sciences, vol. 60. Springer, Berlin (1991)
Namba, M.: Branched coverings and algebraic functions. Pitman Research Notes in Mathematics Series, vol. 161. Longman, Wiley, New York (1987)
Nevanlinna R.: Zur Theorie der meromorphen Funktionen. Acta Math. 46, 1–99 (1925)
Rousseau, E.: Hyperbolicity of geometric orbifolds (in preparation)
Zalcman L.: Normal families: new perspectives. Bull. Am. Math. Soc. (N.S.) 35(3), 215–230 (1998)
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Campana, F., Winkelmann, J. A Brody theorem for orbifolds. manuscripta math. 128, 195–212 (2009). https://doi.org/10.1007/s00229-008-0231-6
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DOI: https://doi.org/10.1007/s00229-008-0231-6