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Aspherical Kähler Manifolds with Solvable Fundamental Group

Oliver Baues·Vicente Cortés
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Abstract

We survey recent developments which led to the proof of the Benson-Gordon conjecture on Kähler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a Kähler manifold which is a homotopy torus is a biholomorphic map. The latter result then implies the classification of compact aspherical Kähler manifolds with (virtually) solvable fundamental group up to biholomorphic equivalence. They are all biholomorphic to complex manifolds which are obtained as a quotient of $\bbC^n$ by a discrete group of complex isometries.

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Oliver Baues, Vicente Cortés. 2006-01-25. Aspherical Kähler Manifolds with Solvable Fundamental Group. https://arxiv.org/abs/math/0601616

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