O'Grady's tenfolds from stable bundles on hyper-Kähler fourfolds

We provide a modular construction of the Laza–Saccà–Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-Kähler manifolds of type OG10, realized as moduli spaces of stable bundles on hyper-Kähler manifolds of type ${\mathrm{K}3}^{[2]}$.