Aspherical Kähler Manifolds with Solvable Fundamental Group

Details Aspherical Kähler Manifolds with Solvable Fundamental Group Aspherical Kähler Manifolds with Solvable Fundamental Group

2006-01-25

arxiv.org/abs/math/0601616v1

Mathematics

Differential Geometry

Scientific paper

We survey recent developments which led to the proof of the Benson-Gordon conjecture on K\"ahler quotients of solvable Lie groups. In addition we prove that the Albanese morphism of a K\"ahler manifold which is a homotopy torus is a biholomorphic map. The latter result then implies the classification of compact aspherical K\"ahler 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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