Prepotentials for local mirror symmetry via Calabi-Yau fourfolds

We outline a simple computational strategy which allows us to define a prepotential for local Calabi-Yau manifolds. The construction is based on a natural procedure which associates a noncompact Calabi-Yau fourfold to a local threefold, and is effective on any space of type K_S, where S is a complex surface. We then develop techniques for reducing problems not of this type to the K_S case. In addition, we provide a method of calculating previously conjectured triple intersection numbers on K_S geometries