Displaying similar documents to “On the universal coverings of algebraic surfaces”

Compact quotients of large domains in complex projective space

Finnur Lárusson (1998)

Annales de l'institut Fourier

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We study compact complex manifolds covered by a domain in n -dimensional projective space whose complement E is non-empty with ( 2 n - 2 ) -dimensional Hausdorff measure zero. Such manifolds only exist for n ≥ 3 . They do not belong to the class 𝒞 , so they are neither Kähler nor Moishezon, their Kodaira dimension is - ∞ , their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds,...

On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi (2010)

Annales de l’institut Fourier

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If a smooth projective variety X admits a non-degenerate holomorphic map ℂ → X from the complex plane ℂ , then for any finite dimensional linear representation of the fundamental group of X the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

Ngaiming Mok (2000)

Annales de l'institut Fourier

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We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then H 1 ( G a m m a , Φ ) ≠ 0 for some unitary representation Φ . By our earlier work there exists a d -closed holomorphic 1-form with coefficients twisted by some unitary representation Φ ' , possibly non-isomorphic to Φ . Taking norms we obtains...