2006/01/25 by Oliver Baues, Vicente Cortés, Baues, Oliver +1 · 1 citation
Mathematics · #22E25 #22E40 #53C55 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:22E25 #msc:22E40 #msc:53C55
paper · pdf · doi:10.48550/arxiv.math/0601616
arxiv created 2006/01/25 · openalex publication_date 2006/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \bbCn by a discrete group of complex isometries.