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Geometric Realizations of Uniformization of Conjugates of Hermitian Locally Symmetric Manifolds

  • Ngaiming Mok
  • Sai Kee Yeung
Part of the The University Series in Mathematics book series (USMA)

Abstract

Let Γ be a bounded symmetric domain, Γ ⊂ Aut(Ω) a torsion-free discrete group of holomorphic automorphisms such that the quotient manifold X = Ω/Γ is of finite volume with respect to the Bergman metric. The manifold X is either algebraic or biholomorphic to a quasi-projective variety, according to Satake, Baily, and Borel [3, 22] for the higher-rank case and to Siu and Yau [24] for the rank-1 case. Fix an embedding of X into a projective space PN and identify X with such a variety. Let σ ∈ Gal(C/Q, and let X σ denote the quasi-projective variety obtained by applying σ to the defining equations of X in P N . By a theorem of Kazhdan [11] in the compact case and a theorem of Borovoy and Kazhdan [5,12] in the general case, X σ ≅ Ω/Γ σ for some torsion-free discrete group of holomorphic automorphisms Γ σ ⊂ Aut(Ω) such that X σ is of finite volume with respect to the Bergmann metric.

Keywords

Vector Bundle Line Bundle Hermitian Manifold Chern Number Holomorphic Automorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Ngaiming Mok
    • 1
  • Sai Kee Yeung
    • 2
  1. 1.Centre d’OrsayUniversité de Paris-SudOrsay CedexFrance
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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