Hypermultiplets, hyper-Kahler cones and quaternion-Kahler geometry

We study hyper-Kahler cones and their corresponding quaternion-Kahler space s. We present a classification of 4(n - 1)-dimensional quaternion-Kahler sp aces with n abelian quaternionic isometries, based on dualizing superconfor mal tensor multiplets. These manifolds characterize the geometry of the hyp ermultiplet sector of perturbative moduli spaces of type-II strings compact ified on a Calabi-Yau manifold. As an example of our construction, we study the universal hypermultiplet in detail, and give three inequivalent tensor multiplet descriptions. We also comment on the construction of quaternion- Kahler manifolds that may describe instanton corrections to the moduli spac e.