Title: Towards a modular construction of OG10

Abstract: Constructing hyper-Kähler manifolds is a challenging problem. Up to deformations, all the known examples arise from moduli spaces of sheaves on symplectic surfaces. It is natural to wonder whether moduli spaces on higher dimensional hyper-Kähler manifolds are also hyper-Kähler. This is very difficult to understand, even in specific examples, and not much is known. In this talk, I will report on an ongoing project aimed at realizing the Laza—Saccà—Voisin compactification of the intermediate Jacobian fibration as a moduli space of stable bundles on a hyper-Kähler fourfold.