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The Debarre-Voisin hyperk\"ahler 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 cubicfourfolds. In this article, we study several trivectors whose associatedDebarre-Voisin variety is degenerate, in the sense that it is either reducibleor has excessive dimension. We show that the Debarre-Voisin varietiesspecialize, along general $1$-parameter degenerations to these trivectors, tovarieties isomorphic or birationally isomorphic to the Hilbert square of a K3surface.

Hilbert squares of K3 surfaces and Debarre-Voisin varieties