For an artinian local ring R with perfect residue field we define higher displays over the small Witt ring. The second crystalline cohomology of a variety of K3-type X (for example the Hilbert schemes of zero-dimensional subschemes of a K3-surface) is equipped with the additional structure of a 2-display. Then we extend the Grothendieck-Messing lifting theory from p-divisible groups to such varieties: The deformations of X over a nilpotent pd-thickening correspond uniquely to selfdual liftings of the associated Hodge-filtration. For the proof we give an algebraic definition of the Beauville-Bogomolov-Form on the second de Rham cohomology of X and show that for ordinary varieties the deformations of X correspond uniquely to selfdual deformations of the 2-display endowed with its Beauville-Bogomolov form. This is joint work with Thomas Zink.