Lucas Libassi : Cubic threefolds and hyperkähler manifolds with a non-symplectic automorphism

In a paper of 2019 Boissière–Camere–Sarti prove that there exists an isomorphism between the moduli space of smooth cubic threefolds and the moduli space of hyperkähler fourfolds of K3[2]-type with a non-symplectic automorphism of order three, whose invariant lattice is generated by a class of square 6. Then, they study the degeneration of the automorphism along the locus of the generic nodal degeneration of a cubic threefold, showing that there exists a birational map from this locus to some moduli space of hyperkähler fourfolds of K3[2]-type with a non-symplectic automorphism of order three belonging to a different family. I will present a generalization of their result to some non-generic nodal cases.