Classification of Albeian Fibered Hyper-Kahler Fourfolds

The aim of this project is the study of hyper-Kaehler manifolds. We wish to prove finiteness of their deformation types, classify the fibrations which occur and explore new examples. Another direction of this project is constructing mirror dual Calabi-Yau manifolds. In attacking the problems we use the methods of twistor bundles, Hilbert schemes and deformation theory. Hyper-Kaehler manifolds are an important mathematical object both in complex differential geometry and mathematical physics. Together with other basic building blocks, which have been studied and understood quite well through the years, these manifolds constitute "special holonomy manifolds". Our approach uses special properties which arise in hyper-Kaehler geometry such as "fibrations".