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

Abstract

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 ${K3}^{[2]}$.

v.2 added Lemma 3.2 for clarity and corrected typos. 52 pages