Hypermultiplets, Hyperkaehler Cones and Quaternion-Kaehler Geometry

We study hyper-Kaehler cones and their corresponding quaternion-Kaehler spaces. We present a classification of 4(n-1)-dimensional quaternion-Ka spaces with n abelian quaternionic isometries, based on dualizing superconformal tensor multiplets. These manifolds characterize the geometry of the hypermultiplet sector of perturbative moduli spaces of type-II strings compactified 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-Kaehler manifolds that may describe instanton corrections to the moduli space. (author)