K\"ahler Solvmanifolds

Abstract

Compact K\"ahler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact K\"ahler solvmanifolds are tori is deduced from this. The main ingredient in the proof is a restriction theorem for polycyclic K\"ahler groups proved by Nori and the author.

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