Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices

Eberhard Oeljeklaus; Christina Schmerling

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 1, page 197-210
  • ISSN: 0373-0956

Abstract

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Let D be a bounded symmetric domain in ℂ 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.

How to cite

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Oeljeklaus, Eberhard, and Schmerling, Christina. "Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices." Annales de l'institut Fourier 50.1 (2000): 197-210. <http://eudml.org/doc/75412>.

@article{Oeljeklaus2000,
abstract = {Let $D$ be a bounded symmetric domain in $\{\Bbb C\}^\{2\}$ and $\Gamma \subset \{\rm Aut\}^\{0\}D$ an irreducible arithmetic lattice which operates freely on $D$. We prove that the cusp–compactification $\overline\{X\}$ of $X=D/\Gamma $ is hyperbolic.},
author = {Oeljeklaus, Eberhard, Schmerling, Christina},
journal = {Annales de l'institut Fourier},
keywords = {hyperbolicity; quotient surfaces},
language = {eng},
number = {1},
pages = {197-210},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices},
url = {http://eudml.org/doc/75412},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Oeljeklaus, Eberhard
AU - Schmerling, Christina
TI - Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 1
SP - 197
EP - 210
AB - Let $D$ be a bounded symmetric domain in ${\Bbb C}^{2}$ and $\Gamma \subset {\rm Aut}^{0}D$ an irreducible arithmetic lattice which operates freely on $D$. We prove that the cusp–compactification $\overline{X}$ of $X=D/\Gamma $ is hyperbolic.
LA - eng
KW - hyperbolicity; quotient surfaces
UR - http://eudml.org/doc/75412
ER -

References

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  12. [Ko] R. KOBAYASHIEinstein-Kähler metrics on open algebraic surfaces of general type, Tohoku Math. J., 37 (1985), 43-77. Zbl0582.53046MR87a:53102
  13. [Mu] D. MUMFORDHirzebruch's proportionality theorem in the non-compact case, Inv. Math., 42 (1977), 239-272. Zbl0365.14012MR81a:32026
  14. [S] C. SCHMERLINGEine Hyperbolizitätsuntersuchung für reine arithmetische Quotientenflächen symmetrischer beschränkter Gebiete, Dissertation, Bremen, 1997. 
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