Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
Annales de l'Institut Fourier, Tome 50 (2000) no. 1, pp. 197-210.

Soit D un domaine symétrique borné dans 2 et soit Γ Aut 0 D un réseau arithmétique irréductible opérant librement sur D. On démontre que la compactification cuspidale de G/Γ est hyperbolique.

Let D be a bounded symmetric domain in 2 and Γ Aut 0 D an irreducible arithmetic lattice which operates freely on D. We prove that the cusp–compactification X ¯ of X=D/Γ is hyperbolic.

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     title = {Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices},
     journal = {Annales de l'Institut Fourier},
     pages = {197--210},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Oeljeklaus, Eberhard; Schmerling, Christina. Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices. Annales de l'Institut Fourier, Tome 50 (2000) no. 1, pp. 197-210. doi : 10.5802/aif.1751. http://www.numdam.org/articles/10.5802/aif.1751/

[AMRT] A. Ash, D. Mumford, M. Rapoport, Y. Tai Smooth compactification of locally symmetric varieties. Lie groups : History, Frontiers and application, vol. IV, Math. Sci. Press, 1975. | MR | Zbl

[BB] W. Baily, A. Borel Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 422-528. | MR | Zbl

[Bo] A. Borel Introduction aux groupes arithmetiques, Hermann, 1969. | MR | Zbl

[BPV] W. Barth, C. Peters, A. Van De Ven Compact complex surfaces, Erg. d. Mathematik, 3. Folge, Bd. 4, Springer (1984). | MR | Zbl

[Br] R. Brody Compact manifolds and hyperbolicity, Trans. AMS, 235 (1976), 213-219. | MR | Zbl

[Fr1] E. Freitag Eine Bemerkung zur Theorie der Hilbertschen Modulmannigfaltigkeiten hoher Stufe, Math. Z., 171 (1980), 27-35. | MR | Zbl

[Fr2] E. Freitag Hilbert modular forms, Springer, 1990. | MR | Zbl

[GR] H. Grauert, H. Reckziegel Hermitesche Metriken und normale Familien holomorpher Abbildungen, Math. Z., 89 (1965), 108-125. | MR | Zbl

[He] J. Hemperly The parabolic contribution to the number of linearly independent automorphic forms on a certain bounded domain, Amer. J. of Math., 94 (1972), 1078-1110. | MR | Zbl

[Hi] F. Hirzebruch Hilbert modular surfaces, Enseign. Math., (1973), 183-281. | MR | Zbl

[Ho] R.-P. Holzapfel Ball and Surface Arithmetics, Aspects of mathematics, Vol. 29, Vieweg, 1998. | MR | Zbl

[Ko] R. Kobayashi Einstein-Kähler metrics on open algebraic surfaces of general type, Tohoku Math. J., 37 (1985), 43-77. | MR | Zbl

[Mu] D. Mumford Hirzebruch's proportionality theorem in the non-compact case, Inv. Math., 42 (1977), 239-272. | MR | Zbl

[S] C. Schmerling Eine Hyperbolizitätsuntersuchung für reine arithmetische Quotientenflächen symmetrischer beschränkter Gebiete, Dissertation, Bremen, 1997.

[ST] G. Schumacher, K. Takegoshi Hyperbolicity and branched coverings, Math. Ann., 286 (1990), 537-548. | MR | Zbl

[vdG] G. Van Der Geer Hilbert modular surfaces, Erg. d. Math., 3, Folge, Vol. 16, Springer, 1988. | MR | Zbl

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