Parole chiave

• Hyperkähler manifold
• cubic fourfold

Abstract After introducing some open questions in the context of compact Hyperkähler manifolds, I will discuss them for some examples of HK manifolds that can be constructed from cubic fourfolds. In this case various answers can be obtained using projective algebraic geometry of cubic fourfolds. The talk is based on old and new results, as well as some work in progress with different collaborators.