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The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds

Terence Napier, Mohan Ramachandran (1997)

Annales de l'institut Fourier

It is proved that if $M$ is a weakly 1-complete Kähler manifold with only one end, then $H_{c}^{1} (M, 𝒪) = 0$ or there exists a proper holomorphic mapping of $M$ onto a Riemann surface.

The moduli space of Riemann surfaces is Kähler hyperbolic.

McMullen, Curtis T. (2000)

Annals of Mathematics. Second Series

Three-manifolds and Kähler groups

D. Kotschick (2012)

Annales de l’institut Fourier

We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is $ℤ$ or $ℤ \oplus ℤ_{2}$ .

Toeplitz operators, Kähler manifolds, and line bundles.

Foth, Tatyana (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Towards a Mori theory on compact Kähler threefolds III

Thomas Peternell (2001)

Bulletin de la Société Mathématique de France

Based on the results of the first two parts to this paper, we prove that the canonical bundle of a minimal Kähler threefold (i.e. $K_{X}$ is nef) is good,i.e.its Kodaira dimension equals the numerical Kodaira dimension, (in particular some multiple of $K_{X}$ is generated by global sections); unless $X$ is simple. “Simple“ means that there is no compact subvariety through the very general point of $X$ and $X$ not Kummer. Moreover we show that a compact Kähler threefold with only terminal singularities whose canonical...

Two remarks on Kähler homogeneous manifolds

Bruce Gilligan, Karl Oeljeklaus (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.