HILBERT SQUARES OF K3 SURFACES AND DEBARRE-VOISIN VARIETIES
Résumé
Debarre-Voisin hyperkähler fourfolds are built from alternating 3-forms on a 10dimensional 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 1parameter degenerations to these trivectors, to varieties isomorphic or birationally isomorphic to the Hilbert square of a K3 surface.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)