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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.

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