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

Alessio Bottini

Published 2024-11-27Version 1

We provide a modular construction of the Laza--Sacc\`a--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-K\"ahler manifolds of type OG10, realized as moduli spaces of stable bundles on hyper-K\"ahler manifolds of type $\mathrm{K3}^{[2]}$.