ncts

Hyper-Kähler manifolds are higher dimensional analogues of K3 surfaces. While the general theory is well-developed few examples are known, with all the known examples being, up to deformation, related to moduli spaces of semistable sheaves on K3 surfaces. In the 90’s it was observed that moduli spaces of sheaves on higher dimensional hyper-Kähler manifolds are good candidates to be (possibly new examples of) hyper-Kähler themselves. However, due to the high technical difficulties, this approach was ignored until recently. In this talk, I will outline the recent developments of the theory of sheaves on higher dimensional hyper-Kähler manifolds, focusing on a specific example of a 10-dimensional “exceptional” hyper-Kähler manifold realized as a moduli space of sheaves on a hyper-Kähler fourfold.