HILBERT SQUARES OF K3 SURFACES AND DEBARRE-VOISIN VARIETIES

Debarre-Voisin hyperkahler 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.