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Aspherical Kähler manifolds with solvable fundamental group

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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 \(\mathbb{C}^{n}\) by a discrete group of complex isometries.

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Authors and Affiliations

  1. Mathematisches Institut II, Universität Karlsruhe, D-76128, Karlsruhe, Germany

    Oliver Baues

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, D-20146, Hamburg, Germany

    Vicente Cortés

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  1. Oliver Baues
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  2. Vicente Cortés
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Correspondence to Oliver Baues.

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Für Frau Kähler anläßlich von Erich Kählers hundertstem Geburtstag

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Baues, O., Cortés, V. Aspherical Kähler manifolds with solvable fundamental group. Geom Dedicata 122, 215–229 (2006). https://doi.org/10.1007/s10711-006-9089-5

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