Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
Annales de l'Institut Fourier, Tome 50 (2000) no. 1, p. 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.
@article{AIF_2000__50_1_197_0,
     author = {Oeljeklaus, Eberhard and Schmerling, Christina},
     title = {Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {1},
     year = {2000},
     pages = {197-210},
     doi = {10.5802/aif.1751},
     zbl = {0952.32015},
     mrnumber = {2001j:32021},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2000__50_1_197_0}
}
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. https://www.numdam.org/item/AIF_2000__50_1_197_0/

[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 56 #15642 | Zbl 0334.14007

[BB] W. Baily, A. Borel Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math., 84 (1966), 422-528. | MR 35 #6870 | Zbl 0154.08602

[Bo] A. Borel Introduction aux groupes arithmetiques, Hermann, 1969. | MR 39 #5577 | Zbl 0186.33202

[BPV] W. Barth, C. Peters, A. Van De Ven Compact complex surfaces, Erg. d. Mathematik, 3. Folge, Bd. 4, Springer (1984). | MR 86c:32026 | Zbl 0718.14023

[Br] R. Brody Compact manifolds and hyperbolicity, Trans. AMS, 235 (1976), 213-219. | MR 57 #10010 | Zbl 0416.32013

[Fr1] E. Freitag Eine Bemerkung zur Theorie der Hilbertschen Modulmannigfaltigkeiten hoher Stufe, Math. Z., 171 (1980), 27-35. | MR 82c:10033 | Zbl 0445.10023

[Fr2] E. Freitag Hilbert modular forms, Springer, 1990. | MR 91c:11025 | Zbl 0702.11029

[GR] H. Grauert, H. Reckziegel Hermitesche Metriken und normale Familien holomorpher Abbildungen, Math. Z., 89 (1965), 108-125. | MR 33 #2827 | Zbl 0135.12503

[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 53 #11110 | Zbl 0259.32010

[Hi] F. Hirzebruch Hilbert modular surfaces, Enseign. Math., (1973), 183-281. | MR 52 #13856 | Zbl 0285.14007

[Ho] R.-P. Holzapfel Ball and Surface Arithmetics, Aspects of mathematics, Vol. 29, Vieweg, 1998. | MR 2000d:14044 | Zbl 0980.14026

[Ko] R. Kobayashi Einstein-Kähler metrics on open algebraic surfaces of general type, Tohoku Math. J., 37 (1985), 43-77. | MR 87a:53102 | Zbl 0582.53046

[Mu] D. Mumford Hirzebruch's proportionality theorem in the non-compact case, Inv. Math., 42 (1977), 239-272. | MR 81a:32026 | Zbl 0365.14012

[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 91b:32028 | Zbl 0847.32029

[vdG] G. Van Der Geer Hilbert modular surfaces, Erg. d. Math., 3, Folge, Vol. 16, Springer, 1988. | MR 89c:11073 | Zbl 0634.14022