Hilbert squares of K3 surfaces and Debarre-Voisin varieties

Debarre--Voisin HK fourfolds are built from alternating 3-forms on a 10-dimensional complex vector space, which we call trivectors. They are analogous to the Beauville--Donagi fourfolds associated with cubic fourfolds. In this article, we study several trivectors whose associated Debarre--Voisin variety is degenerate, in the sense that it is either reducible or has excessive dimension. We show that the Debarre--Voisin varieties specialize, along general 1-parameter degenerations to these trivectors, to varieties isomorphic or birationally isomorphic to the Hilbert square of a K3 surface.